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GED Math : FOIL

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Example Questions

Example Question #41 : Foil

Expand x(x+1)(x+3) , keeping FOIL in the work.

Possible Answers:

$x^{2}+4x+3$

$3x^{2}+3x$

$x^{3}+3x^{2}+3x$

$x^{4}+x^{2}+4x+3$

$x^{3}+4x^{2}+3x$

Correct answer:

$x^{3}+4x^{2}+3x$

Explanation:

There are several ways to solve this problem. We shall keep it so the solution is accessible to FOIL.

This requires an extra step as opposed to more common FOIL questions. Here one is not tasked to multiply two binomials, but two binomials AND a monomial. Multiplication is commutative, meaning we can multiply the terms in any order. It would help to multiply the monomial, x, by one of the binomials, to get it into the form that can be used with FOIL.

So, $x(x+1)=x^{2}+x$

Then, $(x^{2}+x)(x+3)$ $=x^{3}+3x^{2}+x^{2}+3x$ , by FOIL

Simplified, we have $x^{3}+4x^{2}+3x$

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Example Question #42 : Foil

Multiply (x+a)(x-b)

Possible Answers:

$x^{2} -bx+ax-ab$

$x^{2}+ax-bx+ab$

$x^{2}-ab$

$x^{2}-ax+bx-ab$

$x^{2}-abx-ab$

Correct answer:

$x^{2} -bx+ax-ab$

Explanation:

Even though the expression uses letters in the place where it is common to find numbers, we should recognize it is still the multiplication of two binomials, and the FOIL process can be used here.

F: $x\cdot x=x^{2}$

O: $x\cdot -b=-bx$

I: $a\cdot x=ax$

L: $a\cdot -b=-ab$

So we have $x^{2}-bx+ax-ab$

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Example Question #43 : Foil

Expand the expression (x + 4)(x-6)

Possible Answers:

$x^{2} - 2x - 24$

$x^{2}-24x-2$

$x^{2} - 2x -2$

$x^{2} +2x-24$

$x^{2}-24x-24$

Correct answer:

$x^{2} - 2x - 24$

Explanation:

You can use the FOIL method to expand the expression

F:First

O: Outer

I: Inner

L:Last

L-Last

(x+6)(x-4)

F: $x\cdot x=x^{2}$

O: $x\cdot -4=-4x$

I: $6\cdot x=6x$

L: $6\cdot -4=-24$

$x^{2} - 4x + 6x - 24 = x^{}2-2x-24$

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Example Question #41 : Foil

Simplify the following with FOIL

(2x+1)(3x-4)

Possible Answers:

6x^2-4

x^2-3x-4

6x^2-5x-4

6x^2-5x+4

6x^2+5x+4

Correct answer:

6x^2-5x-4

Explanation:

Remember, FOIL stands for First-Outer-Inner-Last

Multiply the first terms

$2x\cdot3x=6x^2$

Multiply the outer terms

$2x\cdot-4=-8x$

Multiply the inner terms

$1\cdot3x=3x$

Multiply the last terms

$1\cdot-4=-4$

Now we simply add them all together

6x^2-8x+3x-4

And combine like-terms

6x^2-5x-4

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Example Question #42 : Foil

Expand: (x+1)(x^2-7)

Possible Answers:

x^3+x^2-7x-7

x^3-x^2-7x-7

x^3-x^2+7x-7

None of the above

Correct answer:

x^3+x^2-7x-7

Explanation:

We distribute each term in each parentheses to the terms of the other parentheses.

We get:

x*x^2, x*-7, x*x, 1*-7

Which Simplifies:

x^3, x^2,-7x,-7

We will arrange these from highest to lowest power, and adding a sign in between terms based on the coefficient of each term:

So, the answer is x^3+x^2-7x-7

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GED Math : FOIL

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #41 : Foil

Example Question #42 : Foil

Example Question #43 : Foil

Example Question #41 : Foil

Example Question #42 : Foil

All GED Math Resources

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