Question

Factor Perfect Square Trinomials In the following exercises, factor.

$2y^3-16y^2+32y$

Short answer

On factorization we get$2y{(y-4)}^2$

Step-by-step solution

Step 1. Given information

An expression is given as$2y^3-16y^2+32y$

Step 2. Factorization

Use square property $(a-b{)}^2=a^2+b^2-2ab$

First convert the expression into the standard form,

$$\begin{gathered} 2y^3-16y^2+32y \\ =2y(y^2-8y+16) \\ =2y(y^2-2\times 4\times y+{\left(4\right)}^2)=2y{(y-4)}^2 \end{gathered}$$