# How do you write f(x)=4*(x-3)(x+7) into standard form?

Feb 3, 2017

$f \left(x\right) = 4 {x}^{2} + 16 x - 84$

#### Explanation:

You can use the FOIL mnemonic to enumerate all of the combinations you need to add together if you find it helpful:

$f \left(x\right) = 4 \cdot \left(x - 3\right) \left(x + 7\right)$

$\textcolor{w h i t e}{f \left(x\right)} = 4 \left({\overbrace{\left(x\right) \left(x\right)}}^{\text{First"+overbrace((x)(7))^"Outside"+overbrace((-3)(x))^"Inside"+overbrace((-3)(7))^"Last}}\right)$

$\textcolor{w h i t e}{f \left(x\right)} = 4 \left({x}^{2} + 7 x - 3 x - 21\right)$

$\textcolor{w h i t e}{f \left(x\right)} = 4 \left({x}^{2} + 4 x - 21\right)$

$\textcolor{w h i t e}{f \left(x\right)} = 4 {x}^{2} + 16 x - 84$