Q. 384 - Intermediate Algebra

Question

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

$36a^2- 84ab + 49b^2$

Step-by-Step Solution

Answer

The factorisation of the given polynomial is: 

$36a^2-84ab +49b^2={(6a-7b)}^2$

Step 1. Given information

The given polynomial is: 

$36a^2- 84ab + 49b^2$

Step 2. Factorise the polynomial

We know that,

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

For polynomial $36a^2-84ab +49b^2$ we have:

$$\begin{gathered} 36a^2- 84ab + 49b^2 \\ {\left(6a\right)}^2-2\times 6a\times 7b+{\left(7b\right)}^2 [U\sin g {(a-b)}^2=a^2-2ab+b^2] \\ {\left(6a-7b\right)}^2 \end{gathered}$$

Thus, the factorisation of the given polynomial is:

$36a^2-84ab+49b^2={(6a-7b)}^2$

Step 3. check the answer

Multiplying the factors, we get:

$$\begin{gathered} 36a^2-84ab+49b^2={(6a-7b)}^2 \\ 36a^2-84ab+49b^2=\left(6a-7b\left)\right(6a-7b\right) \\ 36a^2-84ab+49b^2=36a^2-84ab+49b^2 \end{gathered}$$

This is true.