Question

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

Answer 1

`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 `color(red)((FOIL))`
= `(y−2)(y+4)`
First Term,
= `(color(blue)(y` `− 2)` `(color(blue)(y)+4)`
Outer Term,
= `(color(blue)(y` `− 2)(y+` `color(blue)(4)`)
Inner Term,
= `(y` `color(blue)(−2)` `)(` `color(blue)(y)` `+4)`
Last Term,
=`(y` `color(blue)(-2)`)`(y` `color(blue)(+4))`

First Term, `y` and `y`
= `y * y` = `color(blue)(y²)`

Outer Term, `y` and `4`
= `y * 4` = `color(blue)(4y)`

Inner Term, `-2` and `y`
= `-2 * y` = `color(blue)( -2y)`

Last Term, `-2` and `+4`
= `-2 * 4` = `color(blue)(-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 `4y` and `-2y`, we get `4y + (-2y)` = `2y`

so the final answer is,

= `color(blue)(y² + 2y -8)`