Question

How do you multiply `(4x + 3) ( 5x - 2)`?

Answer 1

`20x^2+7x-6`

Explanation:

`(color(blue)(4x)color(darkred)(+3))(color(red)(5x)color(green)(-2))`

You proceed to FOIL it:

Where you multiply the `color(blue)"first term"` with the `color(red)"outer term"` then you multiply the `color(blue)"first term"` with the `color(green)"inner term"`:

`(color(blue)(4x))(color(red)(5x))=20x^2`

`(color(blue)(4x))(color(green)(-2))=-8x`

Now you multiply the `color(darkred)"last term"` with the `color(red)"outer term"` then you multiply the `color(darkred)"last term"` with the `color(green)"inner term"`:

`color(darkred)((3))(color(red)(5x))=15x`

`color(darkred)((3))(color(green)(-2))=-6`

Now combine them:

`20x^2-8x+15x-6`

Simplify:

`20x^2+7x-6`

Answer 2

You would have to FOIL it up.
To be exact it is `F^2O^2I^2L^2` or square foil.
FirstXFirst; OuterXOuter; InnerXInner; LastXLast.

Explanation:

We will use this example: `(4x+3)(5x-2)to` using square foil

FXF: `4x xx 5x= 20 x^2`

OXO: `4x xx -2 = -8x`

IXI: `3 xx 5x = 15x`

LXL: 3 xx -2 = -6

Then re-assembling: `(4x+3)(5x-2) = 20x^2 -8x+15x-6`

`(4x+3)(5x-2) = 20x^2 +7x-6`