Question

EXERCISE 2.5
1. Use suitable identities to find the following products:
(i) (x+4)(x+10)
(ii) (x+8) (x-10)
(iii) (3x+4) (3x-5
(iv) (+
2
(v) (3 -- 2x) (3 + 2x)​

Answer 1

Answer:

1)

(i) (x+a)(x+b) = x²+(a+b)x + ab

(x+4)(x+10) = x² + 14x + 40

(ii) (x+a)(x+b) = x²+(a+b)x + ab

{x+8} {x+(-10)} = x² - 2x - 80

(iii) (x+a)(x+b) = x²+(a+b)x + ab

{3x+4} {3x+(-5)} = 9x² - x - 20

(iv) you haven’t mentioned the question properly

(v) (x+y)(x-y) = x²- y²

(3 - 2x) (3 + 2x) = 9 - 4x²

Answer 2

Answer:

(i) (x + 4) (x + 10)

Suitable identity is (x + a) (x + b)

= x2 + (a + b)x + ab (x + 4) (x + 10)

= x2 + (4 + 10)x + (4 × 10)

= x2 + 14x + 40

(ii) (x + 8) (x- 10)

Suitable identity is (x + a) (x + b)

= x2 + (a + b)x + ab (x + 8) (x – 10)

= (x)2 + (8 – 10)x + (8 × -10)

= x2 + (-2)x + (-80)

= x2 – 2x – 80

(iii) (3x + 4) (3x – 5)

Suitable identity is (x + a) (x + b)

= x2 + (a + b)x + ab (3x + 4) (3x – 5)

= (3x)2 + (+4 – 5)3x + (4 x -5)

= 9x2 + (-1)3x + (-20)

= 9x2 – 3x – 20

(iv) Suitable identity is (a + b) (a – b)

= a2 – b2

(v) (3 – 2x) (3 + 2x)

Suitable identity is (a + b) (a – b)

= a2 – b2 (3 – 2x) (3 + 2x)

= (3)2 – (2x)2 = 9 – 4x2 .