# How do you write in standard form y = 4(x + 5) - 2(x + 1)(x + 1)?

Jun 24, 2018

$- 2 {x}^{2} + 18$

#### Explanation:

Since this expression has many parts, I will color-code it and tackle it one by one.

color(purple)(4(x+5))-2color(steelblue)((x+1)(x+1)

For the expression in purple, all we need to do is distribute the $4$ to both terms in the parenthesis. Doing this, we now have

$\textcolor{p u r p \le}{4 x + 20} - 2 \textcolor{s t e e l b l u e}{\left(x + 1\right) \left(x + 1\right)}$

What I have in blue, we can multiply with the mnemonic FOIL, which stands for Firsts, Outsides, Insides, Lasts. This is the order we multiply the terms in.

Foiling $\left(x + 1\right) \left(x + 1\right)$:

• First terms: $x \cdot x = {x}^{2}$
• Outside terms: $x \cdot 1 = x$
• Inside terms: $1 \cdot x = x$
• Last terms: $1 \cdot 1 = 1$

This simplifies to $\textcolor{s t e e l b l u e}{{x}^{2} + 2 x + 1}$. We now have

$\textcolor{p u r p \le}{4 x + 20} - 2 \left(\textcolor{s t e e l b l u e}{{x}^{2} + 2 x + 1}\right)$

Distributing the $- 2$ to the blue terms gives us

$\textcolor{p u r p \le}{4 x + 20} - \textcolor{s t e e l b l u e}{2 {x}^{2} - 4 x - 2}$

Combining like terms gives us

$- 2 {x}^{2} + 18$

We see that our polynomial is in standard form, $a {x}^{2} + b x + c$. Notice that the $x$ terms cancel out, so we don't have a $b x$ term.

Hope this helps!