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Algebra 1 : Distributive Property

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Example Questions

Example Question #71 : How To Use Foil In The Distributive Property

Simplify the following expression: $(2x^{2}+3x)(7x-6)$ .

Possible Answers:

$14x^{3}-9x^{2}+18x$

$14x^{3}+9x^{2}+18x$

$14x^{3}-9x^{2}-18x$

None of the above

$14x^{3}+9x^{2}-18x$

Correct answer:

$14x^{3}+9x^{2}-18x$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given $(2x^{2}+3x)(7x-6)$ , then:

First: $2x^{2}\times7x=14x^{3}$

Outer: $2x^{2}\times-6=-12x^{2}$

Inner: $3x\times\7x=21x^{2}$

Last: $3x\times-6=-18x$

Thus, by FOIL:

$(2x^{2}+3x)(7x-6)$

$=14x^{3}+(-12x^{2})+(21x^{2})+(-18x)$

$=14x^{3}+9x^{2}-18x$

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Example Question #72 : How To Use Foil In The Distributive Property

Simplify the following expression: $(1-x^{2})(8x+1)$ .

Possible Answers:

$-8x^{3}-x^{2}-8x-1$

$8x^{3}+x^{2}-8x-1$

$-8x^{3}-x^{2}-8x+1$

$-8x^{3}-x^{2}+8x+1$

$8x^{3}-x^{2}-8x-1$

Correct answer:

$-8x^{3}-x^{2}+8x+1$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given $(1-x^{2})(8x+1)$ , then:

First: $1\times8x=8x$

Outer: $1\times1=1$

Inner: $-x^{2}\times8x=-8x^{3}$

Last: $-x^{2}\times1=-x^{2}$

Thus, by FOIL:

$(1-x^{2})(8x+1)$

$=8x+1+(-8x^{3})+(-x^{2})$

$=8x+1-8x^{3}-x^{2}$

$=-8x^{3}-x^{2}+8x+1$

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Example Question #73 : How To Use Foil In The Distributive Property

Simplify the expression: (a+b)(b+c+d) .

Possible Answers:

2ab+ac+ad

$ab^{2}+abc+abd$

$ab^{2}+ac+ad + b^{2}+bc+bd$

$a+b^{2}+c+d$

$ab+ac+ad+b^{2}+bc+bd$

Correct answer:

$ab+ac+ad+b^{2}+bc+bd$

Explanation:

Each value within one set of parentheses must be distributed to each value in the other set. To solve this problem, you can distribute (a+b) :

a*(b+c+d)+b*(b+c+d)

$=(ab+ac+ad)+(b^{2}+bc+bd)$

Alternatively, you can distribute (b+c+d) :

b*(a+b)+c*(a+b)+d*(a+b)

$=(ab+b^{2})+(ac+bc)+(ad+bd)$

Then, grouping like factors together, you get the correct answer:

$ab+ac+ad+b^{2}+bc+bd$

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Example Question #11 : Foil

Which terms do the following expressions share when simplified?

Possible Answers:

$q^{2}$ only

$q^{2}$ and

Correct answer:

$q^{2}$ only

Explanation:

(q+9)(q-9) is a special type of factorization.

When simplified, the "middle terms" cancel out, because they are the same value with opposite signs:

(q+9)(q-9)

= (q*q)+(q*-9)+(9*q)+(9*-9)

$=q^{2}{\color{Red} -9q+9q}-81$

$=q^{2}-81$

Expressions in the form (a+b)(a-b) always simplify to $(a^{2}-b^{2})$

At this point, we know that the only possible answers are q2 and -81.

However, now we have to check the terms of the second expression to see if we find any similarities.

(q-9)(q-9)

=(q*q)+(q*-9)+(-9*q)+(-9*-9)

$=q^{2}-9q-9q+81$

$=q^{2}-18q+81$

Here we notice that rather than cancelling out, the middle terms combine instead of cancel. Also, our final term is the product of two negative numbers, and so is positive. Comparing the two simpified expressions, we find that only $q^{2}$ is shared between them.

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Example Question #74 : How To Use Foil In The Distributive Property

Simplify the following expression: (7x-1)(2+5x) .

Possible Answers:

$35x^{2}+9x+2$

$35x^{2}-9x+2$

$35x^{2}-9x-2$

None of the above

$35x^{2}+9x-2$

Correct answer:

$35x^{2}+9x-2$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given (7x-1)(2+5x) , then:

First: $7x\times2=14x$

Outer: $7x\times5x=35x^{2}$

Inner: $-1\times2=-2$

Last: $-1\times5x=-5x$

Thus, by FOIL:

$14x+35x^{2}+(-2)+(-5x)$

$=14x+35x^{2}-2-5x$

$=35x^{2}+9x-2$

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Example Question #75 : How To Use Foil In The Distributive Property

Simplify the following expression: $(3x^{2}+x)(4x+7x)$ .

Possible Answers:

None of the above

$33x^{3}-11x^{2}$

$11x^{3}+33x^{2}$

$33x^{3}+11x^{2}$

$11x^{3}-33x^{2}$

Correct answer:

$33x^{3}+11x^{2}$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given $(3x^{2}+x)(4x+7x)$ , then:

First: $3x^{2}\times4x=12x^{3}$

Outer: $3x^{2}\times7x=21x^{3}$

Inner: $x\times4x=4x^{2}$

Last: $x\times7x=7x^{2}$

Thus, by FOIL:

$12x^{3}+21x^{3}+4x^{2}+7x^{2}$

$=33x^{3}+11x^{2}$

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Example Question #76 : How To Use Foil In The Distributive Property

Simplify the following expression: $(x^{2}-5x)(x^{2}+2)$ .

Possible Answers:

$x^{4}-5x^{3}+2x^{2}-10x$

$x^{4}+5x^{3}+2x^{2}+10x$

$x^{4}-5x^{3}+2x^{2}+10x$

$x^{4}+5x^{3}+2x^{2}-10x$

$x^{4}-5x^{3}-2x^{2}-10x$

Correct answer:

$x^{4}-5x^{3}+2x^{2}-10x$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given $(x^{2}-5x)(x^{2}+2)$ , then:

First: $x^{2}\times x^{2}=x^{4}$

Outer: $x^{2}\times2=2x^{2}$

Inner: $-5x\times x^{2}=-5x^{3}$

Last: $-5x\times2=-10x$

Thus, by FOIL:

$x^{4}+2x^{2}+(-5x^{3})+(-10x)$

$=x^{4}+2x^{2}-5x^{3}-10x$

$=x^{4}-5x^{3}+2x^{2}-10x$

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Example Question #77 : How To Use Foil In The Distributive Property

Simplify the following expression: (2x+7)(7x+2) .

Possible Answers:

None of the above

$14x^{2}+53x-14$

$14x^{2}+53x+14$

$14x^{2}-53x+14$

$14x^{2}-53x-14$

Correct answer:

$14x^{2}+53x+14$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given (2x+7)(7x+2) , then:

First: $2x\times7x=14x^{2}$

Outer: $2x\times2=4x$

Inner: $7\times7x=49x$

Last: $7\times2=14$

Thus, by FOIL:

$14x^{2}+4x+49x+14$

$=14x^{2}+53x+14$

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Example Question #78 : How To Use Foil In The Distributive Property

Simplify the following expression: (9-5x)(x+6) .

Possible Answers:

$-5x^{2}-21x-54$

$-5x^{2}-21x+54$

$-5x^{2}+21x+54$

$-5x^{2}+21x-54$

$5x^{2}-21x+54$

Correct answer:

$-5x^{2}-21x+54$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given (9-5x)(x+6) , then:

First: $9\times x=9x$

Outer: $9\times6=54$

Inner: $-5x\times x=-5x^{2}$

Last: $-5x\times6=-30x$

Thus, by FOIL:

$9x+54+(-5x^{2})+(-30x)$

$=54-5x^{2}-21x$

$=-5x^{2}-21x+54$

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Example Question #79 : How To Use Foil In The Distributive Property

Simplify the following expression: (1-x)(5+10x) .

Possible Answers:

$-10x^{2}+5x-5$

$10x^{2}+5x+5$

$-10x^{2}-5x+5$

$-10x^{2}-5x-5$

$-10x^{2}+5x+5$

Correct answer:

$-10x^{2}+5x+5$

Explanation:

In order to simplify the above expression, we can use the FOIL Method (First, Outer, Inner, Last) to multiply the elements of the expression and add the results. Given (1-x)(5+10x) , then:

First: $1\times5=5$

Outer: $1\times10x=10x$

Inner: $-x\times5=-5x$

Last: $-x\times10x=-10x^{2}$

Thus, by FOIL:

$5+10x+(-5x)+(-10x^{2})$

$=5+5x-10x^{2}$

$=-10x^{2}+5x+5$

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Algebra 1 : Distributive Property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #71 : How To Use Foil In The Distributive Property

Example Question #72 : How To Use Foil In The Distributive Property

Example Question #73 : How To Use Foil In The Distributive Property

Example Question #11 : Foil

Example Question #74 : How To Use Foil In The Distributive Property

Example Question #75 : How To Use Foil In The Distributive Property

Example Question #76 : How To Use Foil In The Distributive Property

Example Question #77 : How To Use Foil In The Distributive Property

Example Question #78 : How To Use Foil In The Distributive Property

Example Question #79 : How To Use Foil In The Distributive Property

All Algebra 1 Resources

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