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

3 Answers
Mar 24, 2018

Answer:

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)#

Mar 24, 2018

Answer:

#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!

Mar 24, 2018

Answer:

#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#