Using FOIL with "Longer" Expressions - HELP

[bballwaterboy]

Homework Statement

Multiply Out:
(x^2 + 3x - 5)(x - 2)

Homework Equations

The Attempt at a Solution

I've only seen the FOIL method of multiplying factors where inside the parenthesis of each factor are two terms. So, I know if you have (x - 3)(x + 5), then you get:

x^2 -3x +5x -15, which simplifies to x^2 +2x - 15

But what do you do when there is a longer expression inside the parentheses, such as above: (x^2 + 3x -5)? My brain gets scrambled looking at how to FOIL this situation if we even can. Can we? If so, how?

 

[ehild]

Homework Statement

Multiply Out:
(x^2 + 3x - 5)(x - 2)

Homework Equations

The Attempt at a Solution

I've only seen the FOIL method of multiplying factors where inside the parenthesis of each factor are two terms. So, I know if you have (x - 3)(x + 5), then you get:

x^2 -3x +5x -15, which simplifies to x^2 +2x - 15

But what do you do when there is a longer expression inside the parentheses, such as above: (x^2 + 3x -5)? My brain gets scrambled looking at how to FOIL this situation if we even can. Can we? If so, how?

You have to multiply all terms inside the first parentheses with all terms inside the second one. This is application of the distributive law to expand a(b+c)=ab + ac. Imagine that (x^2 + 3x - 5)=a. Then a(x-2)=ax-2a. The next step is to expand both (x^2 + 3x - 5)x and 2(x^2 + 3x - 5) and add them. Simplify at the end.

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[Mark44]

I've only seen the FOIL method of multiplying factors where inside the parenthesis of each factor are two terms.

FOIL only makes sense when you are multiplying two binomials (two expressions with two terms each. In case you don't know, FOIL is an acronym: F - the first terms of the two pairs of terms, O - the outer terms of the pairs, I - the inner terms of the pairs, and L - the last terms of the two pairs. As soon as you have more than two terms in either factor, FOIL is no help.

 

[bballwaterboy]

You have to multiply all terms inside the first parentheses with all terms inside the second one. This is application of the distributive law to expand a(b+c)=ab + ac. Imagine that (x^2 + 3x - 5)=a. Then a(x-2)=ax-2a. The next step is to expand both (x^2 + 3x - 5)x and 2(x^2 + 3x - 5) and add them. Simplify at the end.
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Thanks, ehild.

That was helpful. So, in a way it's still the same as before, but you're also multiplying the "middle" term of the longer factor, right? It's just having one extra thing to multiply out it seems. So, if I understand your directions correctly, here's what I get then:

x^3 + 3x^2 -5x ...this is your (x^2 +3x -5)x

-2x^2 -6x +10...this is your -2(x^2 +3x -5)

When we add these together, we get:
x^3 + x^2 -11x +10

Would this be the correct answer? Thanks on last time!

 

[ehild]

When we add these together, we get:
x^3 + x^2 -11x +10

Would this be the correct answer? Thanks on last time!

Yes, it is correct! You are the man! :)