# How do you factor x^2 - 8x + 16?

Jul 6, 2018

color(green)(=> (x-4)^2

#### Explanation:

${x}^{2} - 8 x + 16$

$\implies {x}^{2} - \left(2 \cdot 4 \cdot x\right) + {4}^{2}$

It’s in the form ${a}^{2} - 2 a b + {b}^{2} = {\left(a - b\right)}^{2}$

$\therefore \implies {\left(x - 4\right)}^{2}$

Jul 6, 2018

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

#### Explanation:

Given: ${x}^{2} - 8 x + 16$.

We find two numbers, say $a$ and $b$, such that $a + b = - 8$ and $a b = 16$.

Mentally, I see that $a = b = - 4$. Checking, $\left(- 4\right) + \left(- 4\right) = - 8 , - 4 \cdot - 4 = 16$.

Now, we split it into:

$= {x}^{2} + a x + b x + 16$

$= {x}^{2} - 4 x - 4 x + 16$

$= x \left(x - 4\right) - 4 \left(x - 4\right)$

$= \left(x - 4\right) \left(x - 4\right)$

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