Rs Aggarwal 2020 2021 Solutions for Class 8 Maths Chapter 6 Operations On Algebraic Expressions are provided here with simple step-by-step explanations. These solutions for Operations On Algebraic Expressions are extremely popular among Class 8 students for Maths Operations On Algebraic Expressions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2020 2021 Book of Class 8 Maths Chapter 6 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2020 2021 Solutions. All Rs Aggarwal 2020 2021 Solutions for class Class 8 Maths are prepared by experts and are 100% accurate.

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

    8ab-5ab    3ab  -ab
________

   5ab
​

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

    7x-3x    5x  -x-2x
_____
  6x

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

3a - 4b + 4c2a + 3b - 8c  a - 6b +  c
___________
6a -7b-3c

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

    5x-8y+2z-2x-4y+3z  -x+6y- z   3x-3y-2z   5x-9y+2z

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise, we get:

       6ax-2by+ 3cz-11ax+ 6by-  cz  -2ax-3by+10cz   - 7ax+  by+12cz

Page No 84:

Answer:

On arranging the terms of the given expressions in the descending powers of x and adding column-wise:

     2x3- 9x2+  0x+8   0x3+ 3x2 - 6x-5   7x3+ 0x2-10x+1-4x3-5x2+ 2x+3     5x3-11x2-14x+7

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and adding column-wise:

    6p+  4q - r+3-5p+  0q+2r-6-7p+11q+2r-1   0p+  2q-3r+4-6p+17q+0r+0=-6p+17q

Page No 84:

Answer:

On arranging the terms of the given expressions in the descending powers of x and adding column-wise:

4x2+4y2-7xy-3 x2+ 6y2-8xy+02x2-5y2-2xy+67x2+5y2-17xy+3

Page No 84:

Answer:

On arranging the terms of the given expressions in the descending powers of x and subtracting:

-5a2b   3a2b--8a2b

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

                     6pq   -8pq   +                  14pq

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

     -8abc -2abc  +     -6abc

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

  -11p -16p +     5p

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

     3a-4b- c +6    2a-5b+2c-9 -    +     -    +      a + b-3c+15

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

      p-2q-5r-8-6p+  q+3r+8+    -     -   -   7p-3q-8r-16   

Page No 84:

Answer:

On arranging the terms of the given expressions in the descending powers of x and subtracting column-wise:

   3x3-x2+2x-4  x3+3x2-5x+4-    -    +    -  2x3-4x2+7x-8

Page No 84:

Answer:

Arranging the terms of the given expressions in the descending powers of x and subtracting column-wise:

     4y4-2y3-6y2-y+5   5y4-3y3+2y2+y-1 -     +    -     -   +   -y4+ y3- 8y2-2y+6

Page No 84:

Answer:

Writing the terms of the given expressions (in the same order) in the form of rows with like terms below each other and subtracting column-wise:

     3p2-4q2-5r2-6 4p2+5q2-6r2+7-    -      +      - -p2-9q2+r2-13

Page No 84:

Answer:

Let the required number be x.
(3a2-6ab-3b2-1)-x=4a2-7ab-4b2+1
(3a2-6ab-3b2-1)-(4a2-7ab-4b2+1)=x

    3a2-6ab-3b2-1 4a2-7ab-4b2+1-     +    +     -  -a2+ ab+   b2-2

∴ Required number = -a2+ab+b2-2

Page No 84:

Answer:

Sides of the rectangle are l and b.
l=5x2-3y2b=x2+2xy
Perimeter of the rectangle is (2l+2b).

Perimeter = 2(5x2-3y2) + 2(x2+2xy)                =10x2-6y2+2x2+4xy     10x2-6y2   2x2         + 4xy    12x2-6y2+4xyHence, the perimeter of the rectangle is 12x2-6y2+4xy.

Page No 84:

Answer:

Let a, b and c be the three sides of the triangle.

∴ Perimeter of the triangle =(a+b+c)

Given perimeter of the triangle = 6p2-4p+9
One side (a)  = p2-2p+1
Other side (b) = 3p2-5p+3
Perimeter = (a+b+c)
(6p2-4p+9)=(p2-2p+1)+(3p2-5p+3)+c6p2-4p+9-p2+2p-1-3p2+5p-3=c(6p2-p2-3p2)+(-4p+2p+5p)+(9-1-3)=c2p2+3p+5 = c

Thus, the third side is 2p2+3p+5.



Page No 87:

Answer:

By horizontal method:
(5x+7)×(3x+4)=5x(3x+4)+7(3x+4)=15x2+20x+21x+28=15x2+41x+28

Page No 87:

Answer:

By horizontal method:

(4x+9)×(x-6)=4x(x-6)+9(x-6)=4x2-24x+9x-54=4x2-15x-54

Page No 87:

Answer:

By horizontal method:

(2x+5)×(4x-3)=2x(4x-3)+5(4x-3)=8x2-6x+20x-15=8x2+14x-15

Page No 87:

Answer:

By horizontal method:

(3y-8)×(5y-1)=3y(5y-1)-8(5y-1)=15y2-3y-40y+8=15y2-43y+8

Page No 87:

Answer:

By horizontal method:

(7x+2y)×(x+4y)=7x(x+4y)+2y(x+4y)=7x2+28xy+2xy+8y2=7x2+30xy+8y2

Page No 87:

Answer:

By horizontal method:

(9x+5y)×(4x+3y)9x(4x+3y)+5y(4x+3y)=36x2+27xy+20xy+15y2=36x2+47xy+15y2

Page No 87:

Answer:

By horizontal method:

(3m-4n)×(2m-3n)=3m(2m-3n)-4n(2m-3n)=6m2-9mn-8mn+12n2=6m2-17mn+12n2

Page No 87:

Answer:

By horizontal method:

(x2-a2)×(x-a)=x2(x-a)-a2(x-a)=x3-ax2-a2x+a3
i.e (x3+a3)-ax(x-a)

Page No 87:

Answer:

By horizontal method:

(x2-y2)×(x+2y)=x2(x+2y)-y2(x+2y)=x3+2x2y-xy2-2y3i.e(x3-2y3)+xy(2x-y)

Page No 87:

Answer:

By horizontal method:

(3p2+q2)×(2p2-3q2)=3p2(2p2-3q2)+q2(2p2-3q2)=6p4-9p2q2+2p2q2-3q4i.e6p4-7p2q2-3q4

Page No 87:

Answer:

By horizontal method:

(2x2-5y2)×(x2+3y2)=2x2(x2+3y2)-5y2(x2+3y2)=2x4+6x2y2-5x2y2-15y4=2x4+x2y2-15y4

Page No 87:

Answer:

By horizontal method:

(x3-y3)×(x2+y2)=x3(x2+y2)-y3(x2+y2)=x5+x3y2-x2y3-y5=x5-y5+x2y2x-y

Page No 87:

Answer:

By horizontal method:
(x4+y4)×(x2-y2)=x4(x2-y2)+y4(x2-y2)=x6-x4y2+y4x2-y6=x6-y6-x2y2x2-y2

Page No 87:

Answer:

By horizontal method:

x4+1x4×x+1x=x4x+1x+1x4x+1x=x5+x3+1x3+1x5i.e x3(x2+1)+1x31+1x2

Page No 87:

Answer:

By horizontal method:

(x2-3x+7)×(2x+3)=2x(x2-3x+7)+3(x2-3x+7)=2x3-6x2+14x+3x2-9x+21=2x3-3x2+5x+21

Page No 87:

Answer:

By horizontal method:
(3x2+5x-9)×(3x-5)=3x(3x2+5x-9)-5(3x2+5x-9)=9x3+15x2-27x-15x2-25x+45=9x3-52x+45

Page No 87:

Answer:

By horizontal method:
(x2-xy+y2)×(x+y)=x(x2-xy+y2)+y(x2-xy+y2)=x3-x2y+y2x+x2y-xy2+y3=x3+y3

Page No 87:

Answer:

By horizontal method:

(x2+xy+y2)×(x-y)x(x2+xy+y2)-y(x2+xy+y2)=x3+x2y+xy2-x2y-xy2-y3=x3-y3

Page No 87:

Answer:

By horizontal method:

(x3-2x2+5)×(4x-1)=4x(x3-2x2+5)-1(x3-2x2+5)=4x4-8x3+20x-x3+2x2-5=4x4-9x3+2x2+20x-5

Page No 87:

Answer:

By horizontal method:

(9x2-x+15)×(x2-3)=x2(9x2-x+15)-3(9x2-x+15)=9x4-x3+15x2-27x2+3x-45=9x4-x3-12x2+3x-45

Page No 87:

Answer:

By horizontal method:

(x2-5x+8)×(x2+2)=x2(x2-5x+8)+2(x2-5x+8)=x4-5x3+8x2+2x2-10x+16=x4-5x3+10x2-10x+16

Page No 87:

Answer:

By horizontal method:

(x3-5x2+3x+1)×(x2-3)=x2(x3-5x2+3x+1)-3(x3-5x2+3x+1)=x5-5x4+3x3+x2-3x3+15x2-9x-3=x5-5x4+16x2-9x-3

Page No 87:

Answer:

By horizontal method:

(3x+2y-4)×(x-y+2)x(3x+2y-4)-y(3x+2y-4)+2(3x+2y-4)=3x2+2xy-4x-3xy-2y2+4y+6x+4y-8=3x2-2y2-xy+2x+8y-8

Page No 87:

Answer:

By horizontal method:

(x2-5x+8)×(x2+2x-3)=x2(x2-5x+8)+2x(x2-5x+8)-3(x2-5x+8)=x4-5x3+8x2+2x3-10x2+16x-3x2+15x-24=x4-3x3-5x2+31x-24

Page No 87:

Answer:

By horizontal method:

(2x2+3x-7)×(3x2-5x+4)=2x2(3x2-5x+4)+3x(3x2-5x+4)-7(3x2-5x+4)=6x4-10x3+8x2+9x3-15x2+12x-21x2+35x-28=6x4-x3-28x2+47x-28

Page No 87:

Answer:

By horizontal method:

(9x2-x+15)×(x2-x-1)=x2(9x2-x+15)-x(9x2-x+15)-1(9x2-x+15)=9x4-x3+15x2-9x3+x2-15x-9x2+x-15=9x4-10x3+7x2-14x-15



Page No 90:

Answer:

(i) 24x2y3 by 3xy

24x2y3 3xy243x2-1y3-18xy2.

Therefore, the quotient is 8xy2.

(ii) 36xyz2 by −9xz

36xyz2 -9xz36-9x1-1y1-0z2-1-4yz


Therefore, the quotient is 4yz.

(iii)

-72x2y2z by -12xyz-72x2y2z -12xyz-72-12x2-1y2-1z1-16xy

Therefore, the quotient is 6xy.

(iv) −56mnp2 by 7mnp


-56mnp2 7mnp-567m1-1n1-1p2-1-8p

Therefore, the quotient is −8p.

Page No 90:

Answer:

(i) 5m3 − 30m2 + 45m by 5m

(5m3-30m2 +45m) ÷ 5m5m35m-30m25m+ 45m 5mm2 -6m + 9

Therefore, the quotient is m2 6m + 9.

(ii) 8x2y2 − 6xy2 + 10x2y3 by 2xy

(8x2y2 - 6xy2 + 10x2y3 )÷ 2xy8x2y22xy- 6xy22xy+ 10x2y3 2xy4xy - 3y + 5xy2

Therefore, the quotient is 4xy 3y + 5xy2.

(iii) 9x2y − 6xy + 12xy2 by − 3xy

(9x2y - 6xy + 12xy2 )÷ -3xy9x2y-3xy-6xy-3xy+12xy2 -3xy-3x + 2 -4y

Therefore, the quotient is −3x + 2 4y.

(iv) 12x4 + 8x3 − 6x2 by − 2x2

(12x4 + 8x3 - 6x2 )÷ -2x212x4 -2x2+8x3-2x2-6x2-2x2-6x2-4x+32 

Therefore the quotient is −6x2 4x + 3.

Page No 90:

Answer:



Therefore, the quotient is x-2 and the remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is x−2 and the remainder is 0.

Page No 90:

Answer:

(x2 + 12x + 35) by (x + 7)



Therefore, the quotient is x+5 and the remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is 5x-3 and the remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is 2x - 5 and the remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is 3x - 8 and the remainder is 7.

Page No 90:

Answer:



Therefore, the quotient is x2-x-1 and the remainder is 1.

Page No 90:

Answer:



Therefore, the quotient is x2-x+1 and the remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is ( x2 - 3x + 4) and remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is (x-1) and the remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is ( 5x+ 3) and the remainder is (x + 1).

Page No 90:

Answer:



Therefore, the quotient is (x-1) and the remainder is 0.

Page No 90:

Answer:



Therefore, the quotient is ( 4x2+ 3x -2) and the remainder is ( x-1).



Page No 93:

Answer:

(i) We have:

(x+6)(x+6)=(x+6)2=x2+62+2×x×6                [using (a+b)2=a2+b2+2ab]=x2+36+12x

(ii) We have:

(4x+5y)(4x+5y)=(4x+5y)2=4x2+5y2+2×4x×5y          [using (a+b)2=a2+b2+2ab]=16x2+25y2+40xy

(iii) We have:
(7a+9b)(7a+9b)=(7a+9b)2=7a2+9b2+2×7a×9b            [using (a+b)2=a2+b2+2ab]=49a2+81b2+126ab

(iv) We have:
23x+45y23x+45y=23x+45y2=23x2+45y2+2×23x×45y              [using (a+b)2=a2+b2+2ab]=49x2+1625y2+1615xy


(v) We have:
(x2+7)(x2+7)=(x2+7)2=x22+72+2×x2×7             [using (a+b)2=a2+b2+2ab]=x4+49+14x2

(vi) We have:
56a2+256a2+2=56a2+22=56a22+22+2×56a2×2               [using (a+b)2=a2+b2+2ab]=2536a4+4+103a2

Page No 93:

Answer:

(i) We have:
(x-4)(x-4)=(x-4)2=x2-2×x×4+42                   [using (a-b)2=a2-2ab+b2]=x2-8x+16

(ii) We have:
(2x-3y)(2x-3y)=(2x-3y)2=2x2-2×2x×3y+3y2                [using (a-b)2=a2-2ab+b2]=4x2-12xy+9y2

(iii) We have:
34x-56y34x-56y=34x-56y2=34x2-2×34x×56y+56y2           [using (a-b)2=a2-2ab+b2]=916x2-1512xy+2536y2

(iv) We have:
x-3xx-3x=x-3x2=x2-2×x×3x+3x2              [using (a-b)2=a2-2ab+b2]=x2-6+9x2

(v) We have:
13x2-913x2-9=13x2-92=13x22-2×13x2×9+92             [using (a-b)2=a2-2ab+b2]=19x4-6x2+81

(vi) We have:
12y2-13y12y2-13y=12y2-13y2=12y22-2×12y2×13y+13y2            [using (a-b)2=a2-2ab+b2]=14y4-13y3+19y2

Page No 93:

Answer:

We shall use the identities (a+b)2 =a2 +b2 +2ab and (a-b)2 =a2 +b2 -2ab.

(i) We have:
(8a+3b)2=8a2+2×8a×3b+3b2=64a2+48ab+9b2

(ii)We have:
(7x+2y)2=7x2+2×7x×2y+2y2=49x2+28xy+4y2

(iii) We have :
(5x+11)2=5x2+2×5x×11+112=25x2+110x+121

(iv) We have:
a2+2a2=a22+2×a2×2a+2a2=a42+2+4a2

(v) We have:
3x4+2y92=3x42+2×3x4×2y9+2y92=9x162+13xy+4y281

(vi) We have:
(9x-10)29x2-2×9x×10+102=81x2-180x+100

(vii) We have:
(x2y-yz2)2x2y2-2×x2y×yz2+yz22=x4y2-2x2y2z2+y2z4

(viii) We have:
xy-yx2=xy2-2×xy×yx+yx2=x2y2-2+y2x2

(ix) We have:
3m-45n2=3m2-2×3m×45n+45n2=9m2-24mn5+1625n2



Page No 94:

Answer:

(i) We have:

(x+3)(x-3)=x2-9                                [using (a+b)(a-b)=a2-b2]

(ii) We have:

(2x+5)(2x-5)=4x2-25                              [using (a+b)(a-b)=a2-b2]

(iii) We have:

(8+x)(8-x)=64-x2                                 [using (a+b)(a-b)=a2-b2]

(iv) We have:

(7x+11y)(7x-11y)=49x2-121y2                        [using (a+b)(a-b)=a2-b2]

(v) We have:

5x2+34y25x2-34y2=25x4-916y4                       [using (a+b)(a-b)=a2-b2]

(vi) We have:

4x5-5y34x5+5y3=16x225-25y29                     [using (a+b)(a-b)=a2-b2)]

(vii) We have:
x+1xx-1x=x2-1x2                            [using (a+b)(a-b)=a2-b2]

(viii) We have:
1x+1y1x-1y=1x2-1y2                      [using (a+b)(a-b)=a2-b2]

(ix) We have:
2a+3b2a-3b=4a2-9b2                     [using (a+b)(a-b)=a2-b2]

Page No 94:

Answer:

We shall use the identity (a+b)2 =a2 +b2 +2ab.

(i)
542=(50+4)2=502+2×50×4+42=2500+400+16=2916

(ii)
822=(80+2)2=802+2×80×2+22=6400+320+4=6724

(iii)
1032=(100+3)2=1002+2×100×3+32=10000+600+9=10609

(iv)
7042=(700+4)2=7002+2×700×4+42=490000+5600+16=495616

Page No 94:

Answer:

We shall use the identity (a-b)2 = a2 +b2 -2ab.

(i)
692=(70-1)2=702-2×70×1+1=4900-140+1=4761

(ii)
782=(80-2)2=802-2×80×2+4=6400-320+4=6084

(iii)
1972=(200-3)2=2002-2×200×3+9=40000-1200+9=38809

(iv)
9992=(1000-1)2=10002-2×1000×1+1=1000000-2000+1=998001

Page No 94:

Answer:

We shall use the identity (a-b) (a+b)=a2 - b2.

(i)
(82)2-(18)2=(82-18)(82+18)=(64)(100)=6400

(ii)
(128)2-(72)2=(128-72)(128+72)=(56)(200)=11200

(iii)
197×203=(200-3)(200+3)=2002-32=40000-9=39991

(iv)
198×198-102×10296=1982-102296=(198-102)(198+102)96=(96)(300)96=300

(v)
(14.7×15.3)=(15-0.3)×(15+0.3)=(15)2-(0.3)2=225-0.09=224.91

(vi)
(8.63)2-(1.37)2=(8.63-1.37)(8.63+1.37)=(7.26)(10)=72.6

Page No 94:

Answer:

9x2 + 24x + 16Given, x = 123x2 + 2 3x4 + 42  3x + 42312+4236 + 42402 = 1600

Therefore, the value of the expression (9x2 + 24x + 16), when x = 12, is 1600.

Page No 94:

Answer:

64x2+81y2+144xyGiven: x=11  y =438x2 + 9y2 + 28x9y8x +9y 28(11) +9(43)288 +122100210000
                                                                                                                                               
Therefore, the value of the expression (64x2 + 81y2 + 144xy), when x = 11 and y = 43, is 10000.y=43

Page No 94:

Answer:

36x2+25y2-60xyx=23, y=15=6x2 + 5y2 - 26x5y=6x - 5y2=6(23) -5(15)2=4 - 12=329

Page No 94:

Answer:

(i)  x+1x= 4Squaring both the sides:x+1x2= 42x2+1x2+2x1x= 16x2+1x2+2 =16x2+1x2=16-2x2+1x2= 14

Therefore, the value of  x2+1x2 is 14.

x2 + 1x2 = 14Squaring both the sides:x4 + 1x4+2x21x2= 142x4 + 1x4+2 = 196x4 + 1x4 = 196-2x4 + 1x4=194

Therefore, the value of x4 + 1x4 is 194.

Page No 94:

Answer:

(i)  x-1x= 5Squaring both the sides:x-1x2= 52x2+1x2-2x1x= 25x2+1x2-2 =25x2+1x2=25+2x2+1x2= 27Therefore, the value of x2+1x2 is  27.

x2 + 1x2 = 27Squaring both the sides:x4 + 1x4-2x21x2= 272x4 + 1x4-2 = 729x4 + 1x4 = 729+2x4 + 1x4=731Therefore, the value of x4 + 1x4 is 731.

Page No 94:

Answer:

i x+1x-1x2+1x2-x+x-1x2+1x2-1x2+1x22-122              according to the formula a2-b2 = a+ba-bx4-1.Therefore, the product of x+1x-1x2+1 is x4-1.

ii x-3x+3x2+9x2-32x2+9       according to the formula a2-b2 = a+ba-bx2-9x2+9x22-92                 according to the formula a2-b2 = a+ba-bx4-81Therefore, the product of x-3x+3x2+9 is x4-81.

iii 3x-2y3x+2y9x2+4y23x2-2y29x2+4y2        according to the formula a2-b2 = a+ba-b9x2-4y29x2+4y29x22-4y22                 according to the formula a2-b2 = a+ba-b81x4-16y4.Therefore, the product of 3x-2y3x+2y9x2+4y2 is 81x4-16y4.

iv 2p+32p-34p2+92p2-324p2+9       according to the formula a2-b2 = a+ba-b4p2-94p2+94p22-92                according to the formula a2-b2 = a+ba-b16p4-81.Therefore, the product of 2p+32p-34p2+9 is 16p4-81.

Page No 94:

Answer:

x+y = 12On squaring both the sides:x+y2 = 122x2+y2+2xy = 144x2+y2 = 144 - 2xyGiven:  xy = 14x2+y2 = 144 - 214x2+y2 = 144 - 28x2+y2 = 116Therefore, the value of x2+y2 is 116.

Page No 94:

Answer:

x-y = 7On squaring both the sides:x-y2 = 72x2+y2-2xy = 49x2+y2 = 49 + 2xyGiven: xy = 9x2+y2 = 49 + 29x2+y2 = 49 + 18x2+y2 = 67.Therefore, the value of x2+y2 is 67.

Page No 94:

Answer:

(c) (−6a + 17b)

   6a  +4b  -c   +3          +2b  -3c +4-7a +11b +2c -1-5a            +2c -6-6a +17b+ 0c +0¯



Page No 95:

Answer:

(d) (3p2 + 5q − 9r3 +7)

    7p2 +3q  -2r3 +4   4p2 -2q  +7r3 -3-       +       -      +   3p2+ 5q  -9r3 + 7    ¯

Page No 95:

Answer:

(d) x2 + 2x − 15

x+5x-3xx-3+5x-3x2-3x +5x -15x2+2x-15

Page No 95:

Answer:

(b) (6x2 + 7x − 3)

2x+33x-12x3x-1+33x-16x2-2x +9x-36x2+7x-3

Page No 95:

Answer:

(c) (x2 + 8x + 16)

x+4x+4x+42            (according to the formula a+b2 =a2+2ab+b2)x2+2x4+42x2+8x+16

Page No 95:

Answer:

(d) (x2 − 12x + 36)

x-6x-6x-62                             (according to the formula a-b2 =a2-2ab+b2)x2-2x6+62x2-12x+36

Page No 95:

Answer:

(b) (4x2 − 25)

2x+52x-52x2-52           according to the formula a+ba-b = a2-b24x2 - 25

Page No 95:

Answer:

(c) −4ab2

8a2b3 ÷ -2ab8-2a2-1b3-1-4ab2

Page No 95:

Answer:

(b) (2x + 1)

Page No 95:

Answer:

(a) (x − 2)

Page No 95:

Answer:

(c) (a4 − 1)

i a+1a-1a2+1a2 -12a2+1       according to the formula a2-b2 = a+ba-ba2-1a2+1a22-122                 according to the formula a2-b2 = a+ba-ba4-1

Page No 95:

Answer:

a) 1x2-1y2

1x+1y1x-1yAccording to the formula a+ba-b=a2-b2:1x2-1y2(1x21y2)

Page No 95:

Answer:

(c) 23

  x+1x= 5Squaring both the sides:x+1x2= 52x2+1x2+2x1x= 25x2+1x2+2 =25x2+1x2=25-2x2+1x2= 23

Page No 95:

Answer:

(b) 38

x-1x= 6Squaring both the sides:x-1x2= 62x2+1x2-2x1x= 36x2+1x2-2 =36x2+1x2=36+2x2+1x2= 38

Page No 95:

Answer:

(c) 6400

822-182=82 + 1882 - 18=10064=6400                           [using the identity (a-b)(a+b)=a2 -b2]

Page No 95:

Answer:

(a) 39991

197×203200-3200+32002-3240000-939991                   [using the identity (a+b) (a-b) = a2  -b2]

Page No 95:

Answer:

(b) 116

a+b =12Squaring both the sides:a+b2 = 122a2+ b2 +2ab = 144a2+ b2 = 144-2aba2+ b2 = 144 -214a2+ b2 = 144 -28a2+ b2 = 116

Page No 95:

Answer:

(a) 67

a-b =7Squaring both the sides:a-b2 = 72a2+ b2 -2ab = 49a2+ b2 = 49+2aba2+ b2 = 49 +29a2+ b2 =  49+18a2+ b2 = 67

Page No 95:

Answer:

(c) 625

4x2+20x+252x2+22x5+522x + 52210+5220+52252625



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