Question

1) Use suitable identities to find the following products.

i) (x + 5) (x + 2) ii) (x-5)(x-5) iii) (3x +2)(3x-2)

iv) 2 2

2 2

   1 1      

  

x x

x x

v) (1 + x)(1 + x)

2)Evaluate the following products without actual multiplication.

i) 101 × 99 ii) 999 × 999 iii) 1 1 50 49

2 2



iv) 501 × 501 v) 30.5 × 29.5​

Answer 1

Step-by-step explanation:

(1) (x+5)(x+2)

= x×x+x×2+5×x+5×2

= x^2+2x+5x+10

= x^2+7x+10

(2) (x-5)(x-5)

= (x-5)^2

= (x)^2+(5)^2-2×x×5

= (x)^2+25-10x

(3) (3x+2)(3x-2)

= (3x)^2-(2)^2. [(a-b)(a+b)=a^2-b^2]

= 9x^2-4

(5) (1+x)(1+x)

= (1+x)^2

= (1)^2+(x)^2+2×1×x

= 1+x^2+2x