Q.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) (y2+ 32) (y2 - 32)

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

Solution:

(i) Using identity, (x + a)(x + b) = x2 + (a + b)x + ab

(x + 4) (x + 10) = x2 + (4 + 10)x + (4 × 10)

= x2 + 14x + 40

(ii) Using identity, (x + a)(x + b) = x2 +(a + b)x + ab

(x + 8) (x -10) = x2 + {8 +(- 10)}x + {8×(-10)}

 = x2 + (8 - 10)x - 80

 = x2 - 2x - 80

(iii) Using identity, (x + a)(x +b) = x2 +(a + b)x + ab

(3x + 4) (3x - 5)

= (3x)2 + {4 + (-5)}3x + {4×(-5)}

= 9x2 + 3x(4 - 5) - 20

= 9x2 - 3x - 20

(iv) Using identity, (x + y) (x -y) = x2 - y2

y2+32y2-32= y22- 322

= y4 - 94

(v) Using identity, (x + y) (x -y) = x2 - y2

(3 - 2x) (3 + 2x) = 32 - (2x)2

= 9 - 4x2