Question

How do you FOIL `(4z-u)(3z+2u)`?

Answer 1

The FOIL'ed version of the factored expression is `12z^2 +5zu-2u^2`

Explanation:

As you may know, FOIL stands for First Outer Inner Last. Using this Mnemonic, we'll work in order.

First:
`4zxx3z=4xx3xxzxxz=12z^2`

Outer:
`4zxx2u=4xx2xxzxxu=8zu`

Inner:
`-uxx3z=-1xx3xxuxxz=-3uz=-3zu`

Last:
`-uxx2u=-1xx2xxuxxu=-2u^2`

Now, let's put them back together in the expression:

`12z^2+8zu-3zu-2u^2`

Finally we combine like terms to get our finished expression:

`12z^2+(8-3)zu-2u^2=color(red)(12z^2+5zu-2u^2)`

Answer 2

`12z^2 +5zu -2u^2`

Explanation:

The FOIL method:

1. `(4z−u)(3z+2u)`
2. `(4z*3z) +(4z * 2u) + (-u*3z) + (-u * 2u)`
3. `12z^2 +8zu -3zu - 2u^2`
4. `12z^2 +5zu -2u^2`

Hope this helps!

Answer 3

`2` `x^2`+`5` `u` `z` `-` `2` `u^2`

Explanation:

`F`= First
`O`= Outside
`I`= Inside
`L`= Last

`(4z-u)` `(3z+2u)`

Since `4z and 3z` are first you multiply them by each other...

`4 * 3` equals `12`
`z * z` equals `z^2`

`4z and 2u` are at the end so you would multiply them together
and get `8uz` it can also be `8zu` but later on you learn that the letter that comes first in the alphabet is usually at the beginning.

The inside would be
`-u and 3z`
In which `-u * 3z` would equal `-3uz`

Finally, you solve the last two...
`-u * 2u`
Which equals `-2u^2`

You're equation should now look like this;
`12z^2+8uz-3uz-2u^2`

Subtract `8uz and 3uz` - They have common variables
You should get `5uz`

Your final equation should look like this;
`12z^2+5uz-2u^2`