Question

Use suitable identities to find the following products
(1) (x + 5) (x + 2)
(ü) (x - 5) (x - 5) (111) (3x + 2)(3x - 2)

(iv)



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

Evaluate the following products without actual multiplication.
1
(1) 101 x 99
(i) 999 x 999
50–x491
1
2
2
iv) 501 x 501
(v) 30.5 x 29.5​

Answer 1

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

(x+a)(x+b) = x^2 +(a+b)x + ab

x^2 +10 x +10

2) (x-5)(x-5)= (x-5)^2

(a-b)^2= a^2 +b^2 +2ab

x^2+25-10x

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

(a+b)(a-b)= a^2 -b^2

(3x)^2 - (2)^2

=> 9x^2 -4

4) (1+x)(1+x)= (1+x)^2

(a+b)^2 = a^2 + b^2 + 2ab

1 +x^2 +2x

5) 100×99

(100+1)(100-1)

(a+b)(a-b)= a^2- b^2

(100)^2 -(1)^2

10000-1

9999

6)999×999

(1000-1)(1000-1)= (1000-1)^2

(a-b)^2= a^2+b^2-2ab

(1000)^2 + (1)^2 - 2(1000)(1)

1000000+1-2000

998001

7) 501×501= (500+1)(500+1)= (500+1)^2

(a+b)^2= a^2+b^2 +2ab

(500)^2 +(1)^2+ 2(500)(1)

250000+1+1000

251001

8) 30.5 × 29.5

(30+0.5)(30-0.5)

( 30)^2 -(0.5)^2

900- 0.25

899.75

Hope it helps!