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S.chand books class 8 maths solution chapter 13 Algebric Identities exercise 13 B

Exercise 13 B


Expand the following :

Question 1

(i) (x+5)2

(ii) (3x+4)2

(iii) (3x+5y)2

(iv) (1+10mn)2


Question 2

(i) (7y-8)2

(ii) (p-2q)2

(iii) (5y-3z)2

(iv) (6a-11b)2


Question 3

(i) (a2+1)2

(ii) (3a2+b2)2

(iii) (xy-4z)2

(iv) (5a2-7b2)2


Question 4

(i) \left(x+\dfrac{1}{x}\right)^2

(ii) \left(2y-\dfrac{1}{2y}\right)^2


Question 5

(i) (1.5p+2q)2

(ii) \left(5p-\dfrac{1}{4q}\right)^2

(iii) (3.2d-5f)2

(iv) \left(2x^2-\dfrac{1}{3x^2}\right)^2


Question 6

Simplify :

(i) (x+3y)2+ (3x+y)2

(ii) (x-2y)2+ (2x-y)2

(iii) (2x+5y)2– (x+3y)2


Question 7

Without actual multiplication , find the square of 

(i) 98

(ii) 1003

(iii) 999

(iv) 10.8

(v) 99.99


Question 8

Simplify :

(i) 7.61×7.61+2×7.61×2.39+2.39×2.39

(ii) 79.01×79.01+2×79.01×20.99+20.99×20.99

(iii) 0.768×0.768-2×0.768×0.568+0.568×0.568


Question 9

State which of the following expansions is a perfect square.

(i) 4m2+4m+1

(ii) 25q2-40q+16

(iii) a2-6ab-9b2

(iv) 4x^2-2+\dfrac{1}{4x^2}


Question 10

What term should be added to each of the following expressions to make it a perfect square ?

(i) 4a2+28a

(ii) 16+8y

(iii) a2-2a

(iv) 9-6x


Question 11

Find the missing term in the following perfect squares.

(i) 9m2-()+64n2

(ii) ()+46x+84

(iii) 25a2+120ab+()

(iv) ()-90xy+81y2


Question 12

Find the value of a2+b2 , when

(i) a+b=9 , ab=20

(ii) a-b=5 , ab=14


Question 13

Find the value of x^2+\dfrac{1}{x^2} , when

(i) x+\dfrac{1}{x}=3

(ii) x-\dfrac{1}{x}=11


Question 14

Find the value of x^4+\dfrac{1}{x^4} , when

(i) x+\dfrac{1}{x}=3

(ii) x-\dfrac{1}{x}=4


Question 15

Find the value of 

(i) m-n , if m+n=7 , mn=12

(ii) l+m , if l-m=3 , lm=7

(iii) p2+q2 , if p-q=6 and p+q=14

(iv) 4ab, if a+b=9 and a-b=5

(v) 4cd(c2+d2) , if c+d=11 , c-d=1


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