Question

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

Answer 1

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`