# How do you factor 16x^2 -40x +25?

May 22, 2016

$\left(4 x - 5\right) \left(4 x - 5\right) = {\left(4 x - 5\right)}^{2}$

#### Explanation:

This is a pretty straight forward question.

We know that $\textcolor{red}{{\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}}$

Compare ${a}^{2} - 2 a b + {b}^{2}$ to $16 {x}^{2} - 40 x + 25$

Lets look at ${a}^{2}$ and ${b}^{2}$

${a}^{2} = 16 {x}^{2}$ and ${b}^{2} = 25$

$\implies a = 4 x$ and $b = 5$

Then, $2 a b = 2 \times 4 x \times 5 = 40 x$, as given in the expression.

Therefore,

$16 {x}^{2} - 40 x + 25$

$= {\left(4 x\right)}^{2} - \left(2 \times 4 x \times 5\right) + {5}^{2}$

$= {\left(4 x - 5\right)}^{2}$

The factors are $4 x - 5 , 4 x - 5$