# What is the standard form of f(x)=8(x+1)^2-(3x+3)^2 ?

Dec 22, 2015

$f \left(x\right) = - {x}^{2} - 2 x - 1$

#### Explanation:

To rewrite the function in standard form, expand the brackets:

$f \left(x\right) = 8 {\left(x + 1\right)}^{2} - {\left(3 x + 3\right)}^{2}$

$f \left(x\right) = 8 \left(x + 1\right) \left(x + 1\right) - \left(3 x + 3\right) \left(3 x + 3\right)$

$f \left(x\right) = 8 \left({x}^{2} + 2 x + 1\right) - \left(9 {x}^{2} + 18 x + 9\right)$

$f \left(x\right) = 8 {x}^{2} + 16 x + 8 - 9 {x}^{2} - 18 x - 9$

$f \left(x\right) = 8 {x}^{2} - 9 {x}^{2} + 16 x - 18 x + 8 - 9$

$f \left(x\right) = - {x}^{2} - 2 x - 1$