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GED Math : FOIL

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Example Question #31 : Foil

Foil the two equations: $\small (x+5)$ and $\small (x-2)$

Possible Answers:

$\small (x^{2}-3x-10)$

$\small (x^2-3x-10)$

$\small (x^{2}+3x+10)$

$\small (x^{2}+3x-10)$

$\small (x^2-10x-3)$

Correct answer:

$\small (x^{2}+3x-10)$

Explanation:

Foiling means to take two equations and merge them into one. It's also the same as saying you want to multiply one equation with another, which is what we'll be doing.

Our two equations are $\small (x+5)$ and $\small (x-2)$ , which is the same as $\small (x+5)\cdot(x-2)$ . In order to multiply these two equations together, you must first multiply the first unit $\small (x)$ in your equation with everything in the second equation, then the second unit $\small (5)$ with everything in your second equation.

Multiply the $\small x$ in the first equation with the $\small x$ from the second equation:

$\small x\cdot x=x^2$

Multiply the $\small x$ in the first equation with the $\small -2$ from the second equation:

$\small x\cdot-2=-2x$

Now multiply the $\small 5$ with the $\small x$ from the second equation:

$\small 5\cdot x=5x$

Multiply the $\small 5$ from the first equation with the $\small -2$ from the second equation:

$\small 5\cdot-2=-10$

We won't multiply the second equation with the first one like we did above, as that would give us the same answers. Take all the answers you got from above and now string them together like so:

$\small x^2+(-2x)+5x+(-10)$

We're almost done, but we seem to be have more than one $\small x$ ; $\small -2x$ and $\small 5x$ . These two terms can be combined like so: $\small -2x+5x=3x$

Since nothing else seems to have more than one of itself, we can now put the equation together. Make sure to go in order of highest power of $\small x$ to the lowest power of $\small x$ .

Your answer is $\small x^2+3x-10$

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Example Question #31 : Foil

On which of the following would one use the FOIL technique?

Possible Answers:

7x - 14

$w^{2}-5w-1$

(t +3)(t-4)

4y(y-2)

$\frac{3x+3}{x+1}$

Correct answer:

(t +3)(t-4)

Explanation:

The FOIL technique is used to multiply or expand two binomials. None of the other expressions represent two binomials. The closest representation would be 4y(y-2) . This expression calls for the multiplication of a binomial and a monomial, so a more straightforward application of the distributive property would work in that case.

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Example Question #61 : Quadratic Equations

Expand (2-h)(7+2h)

Possible Answers:

$-2h^{2}-11h-14$

$-2h^{2}+3h+14$

$-2h^{2}-3h+14$

$-2h^{2}+11h-14$

$14-2h^{2}$

Correct answer:

$-2h^{2}-3h+14$

Explanation:

One can use the FOIL method.

F: $2\cdot7=14$

O: $2\cdot 2h=4h$

I: $-h\cdot7=-7h$

L: $-h\cdot 2h=-2h^{^{2}}$

Adding them up, we get the polynomial $-2h^{^{2}}-3h+14$ , in the customary form of a polynomial.

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Example Question #34 : Foil

Evaluate $(s + 7)^{2}$

Possible Answers:

$s^{2} +14s+49$

$s^{2} + 7s +49$

$s^{2} +49$

$s^{2} + 14s + 14$

$s^{2} +49s+49$

Correct answer:

$s^{2} +14s+49$

Explanation:

$(s+7)^{2} \equiv (s+7)(s+7)$

So FOIL works in this case

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

O: $s\cdot 7=7s$

I: $7\cdot s=7s$

L: $7\cdot 7=49$

$s^{2}+7s+7s+49=s^{2}+14s+49$

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Example Question #35 : Foil

Expand (y+4)(y-4)

Possible Answers:

$y^{2}-16$

$y^{2}+8y-16$

$y^{2}+16$

$y^{2}-8y-16$

$y^{2}-8y+16$

Correct answer:

$y^{2}-16$

Explanation:

This a case to FOIL

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

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

I: $4\cdot y=4y$

L: $4\cdot -4=-16$

$y^{2}-4y+4y-16=y^{2} -16$

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Example Question #36 : Foil

Expand $(x^{2}+2)(x-8)$

Possible Answers:

$x^{2}-6x-8$

$x^{2}+2x-8$

$x^{3}-8x^{2}+2x-16$

$x^{3}-6x^{2}-8$

$x^{3}-8$

Correct answer:

$x^{3}-8x^{2}+2x-16$

Explanation:

Even though there is an $x^{2}$ in one of the expressions, the expression is STILL a binomial, and should be treated as such. FOIL is used with the multiplication of two binomials, so FOIL works here.

F: $x^{2}\cdot x= x^{3}$

O: $x^{2}\cdot -8=-8x^{2}$

I: $2\cdot x=2x$

L: $2\cdot -8=-16$

Add the terms: $x^{3} -8x^{2}+2x-16$

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Example Question #31 : Foil

Multiply (x+y)(r+s) .

Possible Answers:

xyr+xys

xr+xs+yr+ys

xr+ys

x+yr+s

xy+rs

Correct answer:

xr+xs+yr+ys

Explanation:

The FOIL method works because there are two binomials.

F: $x\cdot r=xr$

O: $x\cdot s=xs$

I: $y\cdot r=yr$

L: $y\cdot s=ys$

Adding gives the polynomial xr+xs+yr+ys

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Example Question #38 : Foil

Multiply (6w +1)(w+2)

Possible Answers:

$6w^{^{2}}+2$

$7w^{2}+13w+2$

$6w^{2}+8w+2$

$6w^{_{2}}+13w+2$

$6w^{2}+3$

Correct answer:

$6w^{_{2}}+13w+2$

Explanation:

We can use FOIL:

F: x $=6w^{2}$

O: x =12w

I: x =1w

L: x

$6w^{2}+12w+1w+2=6w^{2}+13w+2$

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Example Question #32 : Foil

What is the degree of the polynomial represented as the product of the following two binomials? $(x^{3}+4)(x^{2}-3)$

Possible Answers:

A polynomial of degree 5.

A polynomial of degree 6.

A polynomial of degree 2

A polynomial of degree 3.

A line.

Correct answer:

A polynomial of degree 5.

Explanation:

When the binomials are expanded, we get $x^{5}-3x^{3}+4x^{2}-12$ . This is a polynomial of degree 5.

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Example Question #40 : Foil

A rectangular prism-shaped box is given as having a width, , a height 5 more than the width, and a length 4 more than 2 times the width. Write a polynomial that represents the area of the box, using FOIL.

Possible Answers:

$2x^{3}-6x^{2}-20x$

$8x^{3}+40x^{2}$

$4x^{3}+22x^{2}+10x$

70x-350

$2x^{3}+14x^{2}+20x$

Correct answer:

$2x^{3}+14x^{2}+20x$

Explanation:

First, we need to establish the dimensions of the box. We have the width, . The length is 4 more than 2 times the width, so we have 2x+4 , and the height is 5 more than the width, so we have x+5 .

We need to find the area. The area of a rectangular prism is given as length times width times height. So, we can write x(2x+4)(x+5)

To set it up using FOIL, it can be arranged as $(x^{2}+5x)(2x+4)$ .

Through FOIL, we get $2x^{3}+4x^{2}+10x^{2}+20x$ , or $2x^{3}+14x^{2}+20x$ .

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GED Math : FOIL

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #31 : Foil

Example Question #31 : Foil

Example Question #61 : Quadratic Equations

Example Question #34 : Foil

Example Question #35 : Foil

Example Question #36 : Foil

Example Question #31 : Foil

Example Question #38 : Foil

Example Question #32 : Foil

Example Question #40 : Foil

All GED Math Resources

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