Question

We want to factor the following expression:

9x^6 + 6x^3y + y^2

Which pattern can we use to factor the expression?
U and V are either constant integers or single-variable expressions.

Choose 1 answer:
A. (U+V)^2 or (U-V)^2
B. (U+V)(U-V)
C. We can't use any of the patterns.

Answer 1

A. (U+V)^2 or (U-V)^2

Explanation:

`9x^6 + 6x^3y + y^2 \\ \\ = {(3 {x}^(3) )}^(2) + 2.(3x^3).y +( y)^2 \\ \\ = \bigg({3 {x}^(3) } + y \bigg)^(2) \\ \\ = \bigg({3 {x}^(3) } + y \bigg) \bigg({3 {x}^(3) } + y \bigg) \\ \\ \\ \\`