Q 165. - Intermediate Algebra

Question

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

$25n^2-120n+144$

Step-by-Step Solution

Answer

The factor of the trinomial is ${\left(5n-12\right)}^2$.

Step 1. Given information.

Consider the trinomial.

$25n^2-120n+144$

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  ${\left(a-b\right)}^2$.

$$\begin{gathered} {\left(5n\right)}^2-2·5n·12+{12}^2 \\ {\left(5n-12\right)}^2 \end{gathered}$$