# How do you factor completely x^2 - 16x + 64?

Jul 2, 2016

$\left(x - 8\right) \left(x - 8\right)$

#### Explanation:

The expression is a quadratic trinomial which is a product of two brackets.. (x +- ?)(x +-?)

In ${x}^{2} \textcolor{b l u e}{-} 16 x \textcolor{red}{+} 64$
Find the factors of 64 which $\textcolor{red}{A D D}$ up to 16.

The signs in the brackets will be $\textcolor{red}{\text{THE SAME}}$,

Both will be $\textcolor{b l u e}{\text{MINUS}}$.

$8 \times 8 = 64 \mathmr{and} 8 + 8 = 16$

These are the factors we need.

$\left(x - 8\right) \left(x - 8\right)$

Jul 2, 2016

${x}^{2} - 16 x + 64 = {\left(x - 8\right)}^{2}$

#### Explanation:

${x}^{2} - 16 x + 64$

= ${x}^{2} - 8 x - 8 x + 64$

= $x \left(x - 8\right) - 8 \left(x - 8\right)$

= $\left(x - 8\right) \left(x - 8\right)$

= ${\left(x - 8\right)}^{2}$