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Algebra 1 : Distributive Property

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Example Questions

Example Question #101 : Distributive Property

Distribute.

3(x+y)

Possible Answers:

3x+y

3xy

3x+3y

x+3y

3+x+y

Correct answer:

3x+3y

Explanation:

When distributing, we multiply the number on the outside with the individual terms inside the parenthesis in order. So first, we multiply and and then since the operation inside the parenthesis is addition, we keep it addition. Finally, we multiply and and we get 3x+3y .

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Example Question #102 : Distributive Property

Distribute.

4(x-y)

Possible Answers:

4xy

4x-y

4x-4y

x-4y

4-x-y

Correct answer:

4x-4y

Explanation:

When distributing, we multiply the number on the outside with the individual terms inside the parenthesis in order. So first, we multiply and and then since the operation inside the parenthesis is subtraction, we keep it subtraction. Finally, we multiply and and we get 4x-4y .

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Example Question #103 : Distributive Property

Distribute.

-5(x+y)

Possible Answers:

-5x-5y

-5x+5y

-5x+y

5x-5y

x-5y

Correct answer:

-5x-5y

Explanation:

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Example Question #104 : Distributive Property

Distribute.

-8(x-y)

Possible Answers:

8x-8y

8x+8y

x+8y

-8x+8y

-8x+y

Correct answer:

-8x+8y

Explanation:

When distributing, we multiply the number on the outside with the individual terms inside the parenthesis in order. So first, we multiply and and then since the operation inside the parenthesis is subtraction, we keep it subtraction. Finally, we multiply and and we get -8x--8y . Two minus signs become plus sign so our answer is now -8x+8y .

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Example Question #105 : Distributive Property

Distribute and simplify.

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

Possible Answers:

-8x^2-14xy+3y^2

8x^2-3y^2

-8x^2+14xy+3y^2

-8x^2-14xy-3y^2

-8x^2-3y^2

Correct answer:

-8x^2-14xy-3y^2

Explanation:

Let's use FOIL to distribute.

F: Multiply first terms in each binomial $\rightarrow 8x^2$

O: Multiply the outer terms from both binomials $\rightarrow 2xy$

I: Multiply the inner terms from both binomials $\rightarrow 12xy$

L: Multiply the last terms in each binomial $\rightarrow 3y^2$

Finally, we add them all up and we get 8x^2+14xy+3y^2 . Since there is a negative sign, we need to distribute it and finally get -8x^2-14xy-3y^2 .

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Example Question #106 : Distributive Property

Distribute and simplify.

-(x-y)(3-x)

Possible Answers:

-x^2-3x-3y-xy

x^2-xy

-x^2-3x+3y+xy

-x^2-xy

x^2-3x+3y-xy

Correct answer:

x^2-3x+3y-xy

Explanation:

Let's use FOIL to distribute.

F: Multiply first terms in each binomial $\rightarrow 3x$

O: Multiply the outer terms from both binomials $\rightarrow -x^2$

I: Multiply the inner terms from both binomials $\rightarrow -3y$

L: Multiply the last terms in each binomial $\rightarrow xy$

Finally, we add them all up and we get 3x+-x^2+-3y+xy . Since there is a negative sign, we need to distribute it. All the plus and minus sign combinations become minus signs and two minus signs become a plus sign. We finally get x^2-3x+3y-xy .

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Example Question #107 : How To Use Foil In The Distributive Property

Simplify the following equation:

$3\left ( 4-2\right )^{^{_{2}}}$

Possible Answers:

Correct answer:

Explanation:

To simplify this equation you must first do what is in parentheses according to PEMDAS.

So, 4-2=2

After this you must square the

So, $2^{2}=4$

And finally you must multiply that by

So, $3\left ( 4\right )=12$

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Example Question #107 : Distributive Property

Expand the following expression:

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

Possible Answers:

$3x^{2}-10$

$3x^{3}+x-10$

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

$3x^{3}-5x^{2}+6x-10$

$3x^{3}+6x-10$

Correct answer:

$3x^{3}-5x^{2}+6x-10$

Explanation:

$(3x-5)(x^{2}+2) = (3x\cdotx^{2})+(3x\cdot2)+(-5\cdotx^{2})+(-5\cdot2)$

Simplifying:

$3x^{3}-5x^{2}+6x-10$

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Example Question #108 : Distributive Property

Multiply:

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

Possible Answers:

$3x^{2}-8x+12$

7x-12

$6x^{2}+9x-20$

$6x^{2}-x+12$

$6x^{^{2}}+x-12$

Correct answer:

$6x^{^{2}}+x-12$

Explanation:

Use FOIL (First, Outside, Inside, Last) to solve:

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

First: $2x\cdot3x=6x^{2}$

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

Inside: $3\cdot3x=9x$

Last: $3\cdot-4=-12$

This gives us: $6x^{2}-8x+9x-12$

Now combine like terms ('s) to get $6x^{2}+x-12$

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Example Question #109 : Distributive Property

Use FOIL to expand the following:

(2x+7)(3x-2)

Possible Answers:

6x^2+17x-14

5x^2-6x-5

6x^2-14x-12

6x^2-17x+14

5x^2+25x+14

Correct answer:

6x^2+17x-14

Explanation:

Using FOIL, we can easily expand the given polynomial:

(2x+7)(3x-2)

6x^2-4x+21x-14

6x^2+17x-14

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Algebra 1 : Distributive Property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #101 : Distributive Property

Example Question #102 : Distributive Property

Example Question #103 : Distributive Property

Example Question #104 : Distributive Property

Example Question #105 : Distributive Property

Example Question #106 : Distributive Property

Example Question #107 : How To Use Foil In The Distributive Property

Example Question #107 : Distributive Property

Example Question #108 : Distributive Property

Example Question #109 : Distributive Property

All Algebra 1 Resources

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