Question

1. Simplify the following using the identity
(x + a)(x + b)= x + (a + b)x+ ab.
(i) (2m + 3)(2m + 6)​

Answer 1

Answer:

(x+ a)(x + b) = x(x + b) + a (x + b)

= x2 + xb + ax + ab

= x2 + (b + a)x + ab

(x - a)(x - b) = x(x - b) - a (x - b)

= x2 - xb - ax + ab

= x2 - (b + a)x + ab(x + a)(x - b) = x(x - b) + a (x - b)

= x2 - xb + ax - ab

= x2 + (a - b)x - ab

(x - a)(x + b) = x(x + b) - a (x + b)

= x2 + xb - ax - ab

= x2 - (a - b)x – ab

Thus, we have

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

(x - a)(x - b) = x2 - (b + a)x + ab

(x + a)(x - b) = x2 + (a - b)x - ab

(x - a)(x + b) = x2 - (a - b)x – ab

(x + a)(x + b) = x2 + (Sum of constant terms)x + Product of constant terms.