Q. 407 - Intermediate Algebra

Question

In the following exercises, factor completely

$16n^2-56mn+49m^2$.

Step-by-Step Solution

Answer

The factors of the given expression are ${(4n-7)}^2$. 

Step 1. Given and explanation

We have $16n^2-56mn+49m^2$.

We know that 

${(a-b)}^2=a^2-2ab+b^2$.

Applying this, we will factorize the given expression.

Step 2. Factorizing the expression.

We have $16n^2-56mn+49m^2$.

Applying the property 

$$\begin{gathered} {(a-b)}^2=a^2-2ab+b^2 \\ 16n^2-56mn+49m^2 \\ ={\left(4n\right)}^2-2\left(7\right)\left(4\right)mn+{\left(7m\right)}^2 \\ ={(4n-7)}^2 \end{gathered}$$