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

Question

State whether the statements are true (T) or false (F).

x² + (a + b)x + ab = (a + b) (x + ab)

Answer 1

False

We need to factorize x² + (a + b)x + ab, by splitting the middle term:

x² + (a + b)x + ab = x² + ax + bx + ab [∵, ax + bx = (a + b)x & ax × bx = abx²]

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

⇒ x² + (a + b)x + ab = (x + a)(x + b)

And (x + a)(x + b) ≠ (a + b)(x + ab)

⇒ x² + (a + b)x + ab ≠ (a + b)(x + ab)