Q. 385 - Intermediate Algebra

Question

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

$40x^2+ 360x + 810$

Step-by-Step Solution

Answer

The factorisation of the given polynomial is 

$40x^2+ 360x + 810=10{(2x+9)}^2$

Step 1. Given information

The given polynomial is: 

$40x^2+ 360x + 810$

Step 2. Factorise the polynomial

We know that, 

${\left(a+b\right)}^2=a^2+2ab+b^2$

For the polynomial $40x^2+ 360x + 810$

Taking $10$ out as common, we get:

$10(4x^2+36x+81)$

Now, simplifying, we get:

$$\begin{gathered} 10[{\left(2x\right)}^2+2\times 2x+9+9^2] \\ 10{(2x+9)}^2 \end{gathered}$$

The factorisation of the given polynomial is $40x^2+ 360x + 810=10{(2x+9)}^2$