Question

Factor Perfect Square Trinomials In the following exercises, factor.

$75u^2+180u+108$

Short answer

On factorization we get$3{(5u+6)}^2$

Step-by-step solution

Step 1. Given information

An expression is given as$75u^2+180u+108$

Step 2. Factorization

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

First convert the expression into the standard form,

$$\begin{gathered} 75u^2+180u+108 \\ =3(25u^2+60u+36) \\ =3({\left(5u\right)}^2+2\times 5u\times 6+{\left(6\right)}^2)=3{(5u+6)}^2 \end{gathered}$$