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Algebra 1 : How to use FOIL in the distributive property

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Example Questions

Example Question #141 : How To Use Foil In The Distributive Property

Find the product. Simplify the answer.

$\displaystyle ( 5x-3 )( 4x+3 )$

Possible Answers:

$20x^{2}+3x+9$ $\displaystyle 20x^{2}+3x+9$

$20x^{2}+3x-9$ $\displaystyle 20x^{2}+3x-9$

$20x^{2}-3x-9$ $\displaystyle 20x^{2}-3x-9$

$20x^{2}+27x-9$ $\displaystyle 20x^{2}+27x-9$

$\displaystyle 9x$

Correct answer:

$20x^{2}+3x-9$ $\displaystyle 20x^{2}+3x-9$

Explanation:

Foil2

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Example Question #142 : Distributive Property

Solve the following using the FOIL method of distribution.

$\displaystyle (x + 1)(2x - 4)$

Possible Answers:

2x^2 +4 $\displaystyle 2x^2 +4$

$\displaystyle 2x^2 + 2x + 4$

$\displaystyle 2x^2 - 4x - 4$

$\displaystyle 2x^2 - 4$

$\displaystyle 2x^2 -2x - 4$

Correct answer:

$\displaystyle 2x^2 -2x - 4$

Explanation:

When solving using FOIL, we solve in the following order:

FIRST

OUTSIDE

INSIDE

LAST

When looking at the problem

$\displaystyle (x + 1)(2x - 4)$

we will solve

FIRST

$({\color{Red} x }+ 1)({\color{Red} 2x} - 4)$ $\displaystyle ({\color{Red} x }+ 1)({\color{Red} 2x} - 4)$

${\color{Red} 2x^2}$ $\displaystyle {\color{Red} 2x^2}$

OUTSIDE

$({\color{Green} x} + 1)(2x {\color{Green} - 4})$ $\displaystyle ({\color{Green} x} + 1)(2x {\color{Green} - 4})$

${\color{Green} -4x}$ $\displaystyle {\color{Green} -4x}$

INSIDE

$(x {\color{Blue} + 1})({\color{Blue} 2x} - 4)$ $\displaystyle (x {\color{Blue} + 1})({\color{Blue} 2x} - 4)$

${\color{Blue} +2x}$ $\displaystyle {\color{Blue} +2x}$

LAST

$(x {\color{Magenta} + 1})(2x {\color{Magenta} - 4})$ $\displaystyle (x {\color{Magenta} + 1})(2x {\color{Magenta} - 4})$

${\color{Magenta} -4}$ $\displaystyle {\color{Magenta} -4}$

Now, we combine the terms and get

${\color{Red} 2x^2}$ $\displaystyle {\color{Red} 2x^2}$ ${\color{Green} -4x}$ $\displaystyle {\color{Green} -4x}$ ${\color{Blue} +2x}$ $\displaystyle {\color{Blue} +2x}$ ${\color{Magenta} -4}$ $\displaystyle {\color{Magenta} -4}$

and simplify

$\displaystyle 2x^2-2x-4$

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Example Question #142 : Distributive Property

Expand: $\displaystyle (3-x)(9-x)$

Possible Answers:

$\displaystyle x^2-6x+27$

$\displaystyle x^2-12x-27$

$\displaystyle x^2-12x+27$

$\displaystyle x^2+6x-27$

$\displaystyle -x^2-6x+27$

Correct answer:

$\displaystyle x^2-12x+27$

Explanation:

Use the following example to distribute the terms.

$\displaystyle (a+b)(c+d) =ac+ad+bc+bd$

Write down the terms for the binomals, $\displaystyle (3-x)(9-x)$.

$\displaystyle (3)(9) + (3)(-x)+(-x)(9)+(-x)(-x)$

Simplify all terms.

$\displaystyle 27-3x-9x+x^2 = x^2-12x+27$

The answer is: $\displaystyle x^2-12x+27$

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Example Question #143 : Distributive Property

Use the FOIL method to expand the following:

$\displaystyle (2x+4)(-x-5)$

Possible Answers:

$\displaystyle -2x^2-20$

DNE $\displaystyle DNE$

$\displaystyle 2x^2-14x-20$

$\displaystyle -2x^2-14x-20$

Correct answer:

$\displaystyle -2x^2-14x-20$

Explanation:

To FOIL, you must remember that foil stands for F-first, O-ouside, I-inside, L-last. This means you must multiply those terms together and then sum them up. Thus,

$\displaystyle (2x+4)(-x-5)$

$\displaystyle (2x)(-x)+(2x)(-5)+(4)(-x)+(4)(-5)$

$\displaystyle -2x^2-10x-4x-20$

$\displaystyle -2x^2-14x-20$

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Example Question #144 : Distributive Property

Expand the following into a single polynomial:

$\displaystyle (x^2+1)(x+3)$

Possible Answers:

$\displaystyle 4x^2+x+3$

$\displaystyle x^3-3x^2+x+3$

$\displaystyle x^3+3x^2+4$

$\displaystyle x^3+3x^2+x+3$

Correct answer:

$\displaystyle x^3+3x^2+x+3$

Explanation:

To simplify the given product of two binomials into a single polynomial, we must FOIL, which states that given the following binomial:

$\displaystyle (a+b)(c+d)=ac+ad+bc+bd$

or in words, the first two terms are multiplied, the last two terms are multiplied, the inner two terms are multiplied, the last two terms are multiplied, and those are all summed together.

For our two binomials, using the above formula, we get

$\displaystyle x^3+3x^2+x+3$

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Example Question #145 : Distributive Property

Multiply and simplify:

$\displaystyle (2x-y)(2x+4)$

Possible Answers:

$4x^{2} - 8x +2xy-4y$ $\displaystyle 4x^{2} - 8x +2xy-4y$

None of the other responses gives the correct answer.

$4x^{2} + 8x -2xy-4y$ $\displaystyle 4x^{2} + 8x -2xy-4y$

$4x^{2} - 8x -2xy-4y$ $\displaystyle 4x^{2} - 8x -2xy-4y$

$4x^{2} - 8x -2xy+4y$ $\displaystyle 4x^{2} - 8x -2xy+4y$

Correct answer:

$4x^{2} + 8x -2xy-4y$ $\displaystyle 4x^{2} + 8x -2xy-4y$

Explanation:

Using the FOIL method, find the following four products:

F (product of the first terms): $2x \cdot 2x = 4x^{2}$ $\displaystyle 2x \cdot 2x = 4x^{2}$

O (product of the outer terms): $2x \cdot 4 = 8x$ $\displaystyle 2x \cdot 4 = 8x$

I (product of the inner terms): $-y \cdot 2x = -2xy$ $\displaystyle -y \cdot 2x = -2xy$

L (product of the last terms): $-y \cdot 4 = -4y$ $\displaystyle -y \cdot 4 = -4y$

Add the terms:

$4x^{2} + 8x -2xy-4y$ $\displaystyle 4x^{2} + 8x -2xy-4y$

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Example Question #142 : Distributive Property

Multiply and simplify:

$\displaystyle (4x+3)(2x-7)$

Possible Answers:

$8x^{2} -34x +21$ $\displaystyle 8x^{2} -34x +21$

$8x^{2} -34x -21$ $\displaystyle 8x^{2} -34x -21$

$8x^{2} -22x +21$ $\displaystyle 8x^{2} -22x +21$

$8x^{2} -22x -21$ $\displaystyle 8x^{2} -22x -21$

None of the other responses gives the correct answer.

Correct answer:

$8x^{2} -22x -21$ $\displaystyle 8x^{2} -22x -21$

Explanation:

Using the FOIL method, find the following four products:

F (product of the first terms): $4x \cdot 2x = 8x^{2}$ $\displaystyle 4x \cdot 2x = 8x^{2}$

O (product of the outer terms): $4x \cdot (-7) = -28x$ $\displaystyle 4x \cdot (-7) = -28x$

I (product of the inner terms): $3 \cdot 2x = 6x$ $\displaystyle 3 \cdot 2x = 6x$

L (product of the last terms): $3 \cdot (-7) = -21$ $\displaystyle 3 \cdot (-7) = -21$

Add the terms and simplify:

$8x^{2} + (-28x )+ 6x + (-21)$ $\displaystyle 8x^{2} + (-28x )+ 6x + (-21)$

$=8x^{2} -22x -21$ $\displaystyle =8x^{2} -22x -21$,

the correct choice.

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Example Question #147 : Distributive Property

Multiply and simplify:

$\left ( 4x+ \frac{1}{2}\right ) (x- 4)$ $\displaystyle \left ( 4x+ \frac{1}{2}\right ) (x- 4)$

Possible Answers:

$4x ^{2} - \frac{33}{2} x+2$ $\displaystyle 4x ^{2} - \frac{33}{2} x+2$

$4x ^{2} - \frac{31}{2} x +2$ $\displaystyle 4x ^{2} - \frac{31}{2} x +2$

$4x ^{2} - \frac{31}{2} x -2$ $\displaystyle 4x ^{2} - \frac{31}{2} x -2$

$4x ^{2} - \frac{33}{2} x -2$ $\displaystyle 4x ^{2} - \frac{33}{2} x -2$

None of the other responses gives the correct answer.

Correct answer:

$4x ^{2} - \frac{31}{2} x -2$ $\displaystyle 4x ^{2} - \frac{31}{2} x -2$

Explanation:

Using the FOIL method, find the following four products:

F (product of the first terms): $4x \cdot x = 4x ^{2}$ $\displaystyle 4x \cdot x = 4x ^{2}$

O (product of the outer terms): $4x \cdot (-4) = -16x$ $\displaystyle 4x \cdot (-4) = -16x$

I (product of the inner terms): $\frac{1}{2} \cdot x = \frac{1}{2} x$ $\displaystyle \frac{1}{2} \cdot x = \frac{1}{2} x$

L (product of the last terms): $\frac{1}{2} \cdot (- 4) = -2$ $\displaystyle \frac{1}{2} \cdot (- 4) = -2$

Add the terms and simplify:

$4x ^{2} +( -16x) + \frac{1}{2} x +(-2)$ $\displaystyle 4x ^{2} +( -16x) + \frac{1}{2} x +(-2)$

$= 4x ^{2} -16x + \frac{1}{2} x -2$ $\displaystyle = 4x ^{2} -16x + \frac{1}{2} x -2$

$= 4x ^{2} - \frac{32}{2} x + \frac{1}{2} x -2$ $\displaystyle = 4x ^{2} - \frac{32}{2} x + \frac{1}{2} x -2$

$= 4x ^{2} - \frac{31}{2} x -2$ $\displaystyle = 4x ^{2} - \frac{31}{2} x -2$

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Example Question #142 : How To Use Foil In The Distributive Property

Find the square of 4x- 7 $\displaystyle 4x- 7$.

Possible Answers:

$16x^{2} - 28x +49$ $\displaystyle 16x^{2} - 28x +49$

$16x^{2} - 28x-49$ $\displaystyle 16x^{2} - 28x-49$

$16x^{2} + 49$ $\displaystyle 16x^{2} + 49$

None of the other responses gives the correct answer.

$16x^{2} - 49$ $\displaystyle 16x^{2} - 49$

Correct answer:

None of the other responses gives the correct answer.

Explanation:

The square of 4x- 7 $\displaystyle 4x- 7$ can be found by setting A = 4x $\displaystyle A = 4x$ and B = 7 $\displaystyle B = 7$ in the following pattern:

$A^{2} - 2AB + B^{2}$ $\displaystyle A^{2} - 2AB + B^{2}$

$= (4x)^{2} - 2 \cdot 4x \cdot 7 + 7 ^{2}$ $\displaystyle = (4x)^{2} - 2 \cdot 4x \cdot 7 + 7 ^{2}$

$= 16x^{2} - 56 x +49$ $\displaystyle = 16x^{2} - 56 x +49$

None of the given responses match this answer.

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Example Question #149 : Distributive Property

Multiply and simplify:

$\left ( \frac{1}{4}x+ \frac{1}{5} y \right )\left ( \frac{1}{4}x- \frac{1}{5} y \right )$ $\displaystyle \left ( \frac{1}{4}x+ \frac{1}{5} y \right )\left ( \frac{1}{4}x- \frac{1}{5} y \right )$

Possible Answers:

$\frac{1}{16}x ^{2} - \frac{1}{20} xy + \frac{1}{25} y ^{2}$ $\displaystyle \frac{1}{16}x ^{2} - \frac{1}{20} xy + \frac{1}{25} y ^{2}$

$\frac{1}{16}x ^{2} - \frac{1}{10} xy + \frac{1}{25} y ^{2}$ $\displaystyle \frac{1}{16}x ^{2} - \frac{1}{10} xy + \frac{1}{25} y ^{2}$

$\frac{1}{16}x ^{2} + \frac{1}{25} y ^{2}$ $\displaystyle \frac{1}{16}x ^{2} + \frac{1}{25} y ^{2}$

$\frac{1}{16}x ^{2} - \frac{1}{25} y ^{2}$ $\displaystyle \frac{1}{16}x ^{2} - \frac{1}{25} y ^{2}$

None of the other responses gives the correct answer.

Correct answer:

$\frac{1}{16}x ^{2} - \frac{1}{25} y ^{2}$ $\displaystyle \frac{1}{16}x ^{2} - \frac{1}{25} y ^{2}$

Explanation:

The produc of the sum and the difference of these two terms can be found by setting $A = \frac{1}{4}x$ $\displaystyle A = \frac{1}{4}x$ and $B = \frac{1}{5} y$ $\displaystyle B = \frac{1}{5} y$ in the following pattern:

$(A +B)(A-B)= A^{2} - B^{2}$ $\displaystyle (A +B)(A-B)= A^{2} - B^{2}$

$\left ( \frac{1}{4}x+ \frac{1}{5} y \right )\left ( \frac{1}{4}x- \frac{1}{5} y \right )$ $\displaystyle \left ( \frac{1}{4}x+ \frac{1}{5} y \right )\left ( \frac{1}{4}x- \frac{1}{5} y \right )$

$= \left ( \frac{1}{4}x \right ) ^{2} - \left ( \frac{1}{5} y \right )^{2}$ $\displaystyle = \left ( \frac{1}{4}x \right ) ^{2} - \left ( \frac{1}{5} y \right )^{2}$

$= \frac{1}{16}x ^{2} - \frac{1}{25} y ^{2}$ $\displaystyle = \frac{1}{16}x ^{2} - \frac{1}{25} y ^{2}$

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Algebra 1 : How to use FOIL in the distributive property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #141 : How To Use Foil In The Distributive Property

Example Question #142 : Distributive Property

Example Question #142 : Distributive Property

Example Question #143 : Distributive Property

Example Question #144 : Distributive Property

Example Question #145 : Distributive Property

Example Question #142 : Distributive Property

Example Question #147 : Distributive Property

Example Question #142 : How To Use Foil In The Distributive Property

Example Question #149 : Distributive Property

All Algebra 1 Resources

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