Q 168. - Intermediate Algebra

Question

In the following exercises, factor completely using the perfect square trinomials pattern.

$25r^2+60rs+36s^2$

Step-by-Step Solution

Answer

The factor of the polynomial is ${\left(5r+6s\right)}^2$.

Step 1. Given information.

Consider the given trinomial.

$25r^2+60rs+36s^2$

Step 2. Formula used

The general formula for pefect square trinomial is $a^2+2ab+b^2={\left(a+b\right)}^2$.

Step 3. Find the factor of perfect square trinomial.

The middle term of the trinomial is negative, so the binomial square will be of the form  ${\left(a+b\right)}^2$.

$$\begin{gathered} {\left(5r\right)}^2+2·5r·6s+{\left(6s\right)}^2 \\ {\left(5r+6s\right)}^2 \end{gathered}$$