# What is the standard form of f(x)=(x+1)(x+3)+(x+5)^2 ?

Mar 8, 2016

$f \left(x\right) = \textcolor{p u r p \le}{2 {x}^{2} + 14 x + 28}$

#### Explanation:

$f \left(x\right) = \left(x + 1\right) \left(x + 3\right) + {\left(x + 5\right)}^{2}$

Simplify.

$f \left(x\right) = \textcolor{red}{\left(x + 1\right) \left(x + 3\right)} + \textcolor{b l u e}{\left(x + 5\right) \left(x + 5\right)}$

FOIL each pair of binomials. $f \left(x\right) = \textcolor{red}{\left(x \cdot x + 3 \cdot x + 1 \cdot x + 1 \cdot 3\right)} + \textcolor{b l u e}{\left(x \cdot x + 5 \cdot x + 5 \cdot x + 5 \cdot 5\right)}$

Simplify.

$f \left(x\right) = \textcolor{red}{{x}^{2} + 3 x + x + 3} + \textcolor{b l u e}{{x}^{2} + 5 x + 5 x + 25}$

Gather like terms.

$f \left(x\right) = \textcolor{red}{{x}^{2}} + \textcolor{b l u e}{{x}^{2}} + \textcolor{red}{3 x} + \textcolor{red}{x} + \textcolor{b l u e}{5 x} + \textcolor{b l u e}{5 x} + \textcolor{red}{3} + \textcolor{b l u e}{25}$

Simplify.

$f \left(x\right) = \textcolor{p u r p \le}{2 {x}^{2} + 14 x + 28}$