Question

The factors of expression a2 + 2ab + b2 are
(a) (a + b) (a – b) (b) (a + b)2
(c) (a – b)2 (d) (a2 + b2)2

Answer 1

The required 'option (b)  $(a + b)^2$' is correct.

Explanation:

The given expression:

$a^2+2ab+b^2$

To find, the factors of expression $a^2+2ab+b^2$ = ?

∴ $a^2+2ab+b^2$

By factorisation method,

$= a^2+ab+ab+b^2$

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

= (a + b)(a + b)

$= (a + b)^2$

∴ The factors of expression $a^2+2ab+b^2$ $= (a + b)^2$

Thus, the required 'option (b)  $(a + b)^2$' is correct.

Answer 2

The factors of expression a² + 2ab + b² are

(a) (a + b) (a – b)

(b) (a + b)² ✓✓

(c) (a – b)²

(d) (a² + b²)²