# How do you factor 7x^2-28 ?

Mar 29, 2017

$7 \left(x - 2\right) \left(x + 2\right)$

#### Explanation:

There is a $\textcolor{b l u e}{\text{common factor}}$ of 7 in both terms which can be taken out.

$\Rightarrow 7 \left({x}^{2} - 4\right) \to \textcolor{red}{\left(1\right)}$

${x}^{2} - 4 \text{ is a " color(blue)"difference of squares}$ which is factorised in general as follows.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{here " a=x" and } b = 2$

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

going back to $\textcolor{red}{\left(1\right)}$

$\Rightarrow 7 {x}^{2} - 28 = 7 \left(x - 2\right) \left(x + 2\right)$

Mar 29, 2017

$= 7 \left(x + 2\right) \left(x - 2\right)$

#### Explanation:

Always look for a common factor first.

It is $7$ in this case.

$7 {x}^{2} - 28 = 7 \left({x}^{2} - 4\right) \text{ } \leftarrow$ this is the difference of squares.

$= 7 \left(x + 2\right) \left(x - 2\right)$

The expression has 3 factors