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Algebra 1 : Distributive Property

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Example Questions

Example Question #3 : Foil

What is the equation that has the following solutions? x=5,-8

Possible Answers:

$x^{2}+5x-60$

$x^{2}+13x-40$

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

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

Correct answer:

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

Explanation:

This is a FOIL-ing problem. First, set up the numbers in a form we can use to create the function.

Take the opposite sign of each of the numbers and place them in this format. (x-5)(x+8)

Multiply the in the first parentheses by the and 8 in the second parentheses respectively to get $x^{2}+8x$

Multiply the in the first parentheses by the and 8 in the second parentheses as well to give us -5x-40 .

Then add them together to get $x^{2}+8x-5x-40$

Combine like terms to find the answer which is $x^{2}+3x-40$ .

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Example Question #3 : Foil

Simplify the following expression.

$(3x^{2}-3)(2x^{3}-8)$

Possible Answers:

$6x^{5}-30x^{2}+24$

$6x^{5}-6x^{3}-24x^{2}+24$

$6x^{5}-6x^{3}-24x^{2}-24$

$6x^{6}-6x^{3}-24x^{2}+24$

$6x^{5}-30x^{2}-24$

Correct answer:

$6x^{5}-6x^{3}-24x^{2}+24$

Explanation:

Simplify using FOIL method.

Remember that multiplying variables means adding their exponents.

F: $3x^{2}*2x^{3} = 6x^{5}$

O: $3x^{2}*(-8) = -24x^{2}$

I: $-3 *2x^{3}=-6x^{3}$

L: -3 *-8= 24

Combine the terms. Note that we cannot simplify further, as the exponents do not match and cannot be combined.

$6x^{5}-6x^{3}-24x^{2}+24$

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Example Question #2 : Distributive Property

$\left ( 3x+2\right )\left ( 2x-5\right )=$

Possible Answers:

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

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

$6x^{2}-11x-10$

$6x^{2}+19x+10$

$6x^{2}+19x -10$

Correct answer:

$6x^{2}-11x-10$

Explanation:

$\textup{FOIL: Product is the sum of the products of the first, outer, inner and last terms:}$

$\left ( 3x+2\right )\left ( 2x-5\right )=$ $3x\ast2x+3x\left ( -5\right )+ 2\ast2x+2\left ( -5\right )$

$6x^{2}-15x+4x-10\;\;\;=\;\;\;6x^{2}-11x-10$

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Example Question #3 : Distributive Property

What are the factors of $x^{2}+11x+24$ ?

Possible Answers:

(x+6)(x+4)

(x+11)(x+13)

(x+8)(x+3)

(x+10)(x+1)

(x+8)(x+4)

Correct answer:

(x+8)(x+3)

Explanation:

To find the factors, you must determine which of the sets of factors result in the polynomial when multiplied together. Using the FOIL method, a set of factors with the form (x+a)(x+b) will result in $x^{2}+ax+bx+ab$ . Applying this format to the given equation of $x^{2}+11x+24$ , a+b must equal 11 and must equal 24. The only set that works is (x+8)(x+3) .

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Example Question #1 : Distributive Property

Expand:

(x+3)(2x-5)

Possible Answers:

$2x^{2}-x+15$

$x^{2}+2x-15$

$x^{2}-2x-15$

$2x^{2}+x-15$

$2x^{2}-2x-15$

Correct answer:

$2x^{2}+x-15$

Explanation:

If you use the FOIL method, you will multiply each expression individually. So, (x+3)(2x-5) becomes (x*2x)+(x*-5)+(3*2x)+(3*-5) , which simplifies to $2x^{2}+x-15$ .

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Example Question #4 : Distributive Property

Simplify the expression below.

$x^{2}y(2x + 3y)$

Possible Answers:

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

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

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

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

$5x^{2}y + 6x^{2}y^{2}$

Correct answer:

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

Explanation:

$x^{2}y(2x + 3y)$

Use the distributive property to simplify the expression. In general, a(b+c) = ab + ac .

$x^{2}y(2x + 3y)=(x^{2}y*2x) + (x^{2}y*3y)$

Now we can begin to combine like terms through multiplication.

$(x^{2}y*2x) + (x^{2}y*3y)$

$(2x^{3}y)+(3x^2y^2)$

We cannot simplify further.

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Example Question #5 : Distributive Property

Multiply the binomials below.

(4x-7)(2x+6)

Possible Answers:

$8x^{2}-42$

$8x^{2}-38x-42$

$8x^{2}-10x-42$

$8x^{2}+10x-42$

$8x^{2}+38x-42$

Correct answer:

$8x^{2}+10x-42$

Explanation:

The FOIL method yields the products below.

First: $4x* 2x=8x^{2}$

Outside: 4x* 6=24x

Inside: -7* 2x=-14x

Last: -7* 6=-42

Add these four terms, and combine like terms, to obtain the product of the binomials.

$8x^{2}+24x+(-14x)+(-42)=8x^{2}+10x-42$

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Example Question #4 : Foil

Factor the expression below.

x^3-3x^2-18x

Possible Answers:

x(x-6)(x-3)

x(x-6)(x+3)

(x^2-6x)(x^2+3x)

x(x+6)(x-3)

Correct answer:

x(x-6)(x+3)

Explanation:

x^3-3x^2-18x

First, factor out an , since it is present in all terms.

x(x^2-3x-18)

We need two factors that multiply to and add to .

-6*3=-18 and -6+3=-3

Our factors are and .

x(x-6)(x+3)

We can check our answer using FOIL to get back to the original expression.

First: (x)(x)=x^2

Outside: (x)(3)=3x

Inside: (x)(-6)=-6x

Last: (-6)(3)=18

Add together and combine like terms.

x^2+3x-6x-18=x^2-3x-18

Distribute the that was factored out first.

x(x^2-3x-18)=x^3-3x^2-18x

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Example Question #2 : Distributive Property

$\textup{What is the value of }\left ( 2p+4\right )\left ( p-5\right )\textup{?}$

Possible Answers:

$2p^{2}-6p-20$

$2p^{2}-p-20$

$2p^{2}-14p-20$

$2p^{2}+6p+20$

$2p^{2}-20p-9$

Correct answer:

$2p^{2}-6p-20$

Explanation:

$\textup{FOIL to distribute:} \left ( 2p+4\right )\left ( p-5\right )= 2p(p)+2p(-5)+4(p)+4(-5)$

$2p^{2}-10p+4p-20\;\;\;\;\;\;\;\;2p^{2}-6p-20$

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Example Question #8 : Distributive Property

Expand:

(x+4)(3x-2)

Possible Answers:

$3x^{2}+10x-8$

$3x^{2}+14x-8$

$x^{2}+10x-8$

$x^{2}+14x+8$

$3x^{2}+10x+8$

Correct answer:

$3x^{2}+10x-8$

Explanation:

To expand (x+4)(3x-2) , use the FOIL method, where you multiply each expression individually and take their sum. This will give you

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

or $3x^{2}+10x-8$

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Algebra 1 : Distributive Property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3 : Foil

Example Question #3 : Foil

Example Question #2 : Distributive Property

Example Question #3 : Distributive Property

Example Question #1 : Distributive Property

Example Question #4 : Distributive Property

Example Question #5 : Distributive Property

Example Question #4 : Foil

Example Question #2 : Distributive Property

Example Question #8 : Distributive Property

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