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

Feb 27, 2016

The standard form of this equation is :
$f \left(x\right) = 5 {x}^{2} + 8 x + 4$

#### Explanation:

The standard form of an equation should look like :
$f \left(x\right) = a {x}^{2} + b x + c$

First, you have to develop the right member : $\left(x + 1\right) \left(x + 3\right) + {\left(- 2 x - 1\right)}^{2}$

$\left[\left(x \cdot x\right) + \left(x \cdot 3\right) + \left(1 \cdot x\right) + \left(1 \cdot 3\right)\right] + \left[{\left(- 2 x\right)}^{2} - 2 \cdot \left(- 2 x \cdot 1\right) + {1}^{2}\right]$
Then, we can simplified it :
$\left[{x}^{2} + 3 x + x + 3\right] + \left[4 {x}^{2} + 4 x + 1\right]$
${x}^{2} + 4 x + 3 + 4 {x}^{2} + 4 x + 1$
$5 {x}^{2} + 8 x + 4$

So, $f \left(x\right) = 5 {x}^{2} + 8 x + 4$