# How do you find the product (y-2)(y+4)?

Feb 15, 2017

color(blue)(y² + 2y -8)

#### Explanation:

using the Distributive Property of Real Numbers,
FOIL METHOD (First Term, Outer Term, Inner Term, and the Last Term)

color(blue)((a+b)(a+b) = a² + 2ab + b²)
color(blue)((a-b)(a+b) = a² - b²)

Answering using the Distributive Property $\textcolor{red}{\left(F O I L\right)}$
= (y−2)(y+4)
First Term,
= (color(blue)(y − 2)$\left(\textcolor{b l u e}{y} + 4\right)$
Outer Term,
= (color(blue)(y − 2)(y+$\textcolor{b l u e}{4}$)
Inner Term,
= (ycolor(blue)(−2))($\textcolor{b l u e}{y}$+4)
Last Term,
=(y$\textcolor{b l u e}{- 2}$)(ycolor(blue)(+4))

First Term, $y$ and $y$
= $y \cdot y$ = color(blue)(y²)

Outer Term, $y$ and $4$
= $y \cdot 4$ = $\textcolor{b l u e}{4 y}$

Inner Term, $- 2$ and $y$
= $- 2 \cdot y$ = $\textcolor{b l u e}{- 2 y}$

Last Term, $- 2$ and $+ 4$
= $- 2 \cdot 4$ = $\textcolor{b l u e}{- 8}$

Plugging all the answers, we get:

= color(blue)(y² + 4y - 2y -8)

always simplify the answer by combining (adding) like terms, the like term is the $4 y$ and $- 2 y$, we get $4 y + \left(- 2 y\right)$ = $2 y$

= color(blue)(y² + 2y -8)