Question

x² + (a + b)x + ab = (a + b)(x + ab)

Options

• True

• False

Answer 1

This statement is False.

Explanation:

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 and 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)