How do you multiply #(7v + 2) ( 5v - 1)#?

1 Answer
Jun 25, 2018

Use the FOIL Method

Explanation:

Explanation 1 (using words)
FOIL is a mnemonic for the standard method of multiplying binomials.

F irst ("first" terms of each binomial are multiplied together)
O uter ("outside" terms are multiplied—that is, the first term of the first binomial and the second term of the second)
I nner ("inside" terms are multiplied—second term of the first binomial and first term of the second)
L ast ("last" terms of each binomial are multiplied)

Given #(7v+2)(5v-1)#

First, we must multiply the first terms of the two binomials, which are #7v# and #5v#, which gives as a result of #35v^2#.

Next, we must multiply the outer terms of the two binomials, which are #7v# and #-1#, which gives as a result of #-7v#.

After this, we must multiply the inner terms of the two binomials, which are #2# and #5v#, which gives as a result of #10v#.

Notice that the product of the Outer and Inner both end in #v#. Thus, these two can be combined. When combine or add these, the result is #3v#, since #(-7v)+10v=3v#

We're nearly complete, we already have #35v^2+3v#.

Last, we must multiply the outer terms of the two binomials, which are #2# and #-1#, which gives as a result of #-2#.

Thus, our final answer is #35v^2+3v-2#.

Explanation 2

#(7v+2)(5v-1)= (7v)(5v)+(7v)(-1)+(2)(5v)+(2)(-1)#
#=35v^2-7v+10v-2#
#=35v^2+3v-2#