Question

Factorize 16x^2 + 16xy + 4y^2. A) (4x + 2y)^2 B) (4x - 2y)^2 C) 4(x + y)^2 D) 4(x - y)^2

Answer 1

A

Explanation:

given

16x² + 16xy + 4y²

an expression factorised as a perfect square has the form

(ax + by)²

= a²x² + 2abxy + b²y²

16x² + 16xy + 4y² ← is in this form

with a² = 16 , b² = 4

so a =
`√(16)` = 4 and b =
`√(4)` = 2

then 2ab = 2(4)(2) = 16

Thus

16x² + 16xy + 4y² = (4x + 2y)² ← in factorised form