Question

How do you multiply `(w + 3) ( 4w - 4)`?

Answer 1

`4w^2 + 8w - 12`

Explanation:

You need to cross multiply each term in the parenthesis on the left by each term in the parenthesis on the right:

`(w*4w) - (4*w) + (3*4w) - (3*4)`

`4w^2 - 4w + 12w - 12`

Now we can combine like terms:

`4w^2 + (-4 + 12)w - 12`

`4w^2 + 8w - 12`

Answer 2

`(w+3)(4w-4)=color(magenta)(4w^2+8w-12)`

Explanation:

There are several ways to to this.
Here are two.

Tabular Multiplication
#{: (xx," | ",w,color(white)("X"),3), ("---",,"------","------","------"), (4w," | ",color(red)(4w^2),,color(green)(12w)), (-4," | ",color(green)(-4w),,color(blue)(-12)), ("---","------","------","------","------"), (,color(red)(4w^2),color(green)(+8w),,color(blue)(-12)) :}#

FOIL `color(black)((w+3)(4w-4)`
#{: ("First terms:", wxx4w,=,color(red)(4w^2)), ("Outside terms:",wxx(-4),=,color(green)(-4w)), ("Inside terms:",3xx4w,=,color(green)(12w)), ("Last terms:",3xx(-4),=,-color(blue)(12)), ("----------------","----------","------","--------"), (,color(red)(4w^2),color(green)(+8w),color(blue)(-12)) :}#

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I have a slight personal preference for the Tabular Form since it is not restricted to multiplication of binomial factors as is FOIL.