# How do you simplify y = 4(x + 5) - 2(x + 1)(x + 1)?

Jul 16, 2016

$y = 4 \left(x + 5\right) - 2 \left(x + 1\right) \left(x + 1\right)$

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

#### Explanation:

We can start off by multiplying the $4$ on the left.

$y = 4 \left(x + 5\right) - 2 \left(x + 1\right) \left(x + 1\right)$

$= 4 x + 20 - 2 {\left(x + 1\right)}^{2}$

Remembering that ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$ we get

$= 4 x + 20 - 2 \left({x}^{2} + 2 x + 1\right)$

The tricky part here is that we have a negative out on front of the $2$ which gets multiplied to every term within the parantheses.

$= \cancel{4 x} + 20 - 2 {x}^{2} \cancel{- 4 x} - 2$

$= 20 - 2 {x}^{2} - 2$

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

Or the equivalent:

$= 2 \left(9 - {x}^{2}\right)$

$= 2 \left(3 - x\right) \left(3 + x\right)$