Question

Which of these statements is a valid perfect square trinomial?

Statement 1: x2 + 4x + 4 = (x + 2)2
Statement 2: a2 + 2ab + ab = (a + b)2

a
Statement 1 and statement 2 are valid.

b
Statement 1 and statement 2 are invalid.

c
Only statement 1 is valid.

d
Only statement 2 is valid.

Answer 1

C

Explanation:

consider the right side

(x + 2)²

= (x + 2)(x + 2) ← expand using FOIL

= x² + 2x + 2x + 4 ← collect like terms

= x² + 4x + 4 = left side

then x² + 4x + 4 is a valid perfect square binomial

x² + 4x + 4 = (x + 2)²

then

x² + 4x + 4

Statement 2

consider the right side

(a + b)²

= (a + b)(a + b) ← expand using FOIL

= a² + ab + ab + b² ≠ left side

then

a² + 2ab + ab is not a valid perfect square binomial