Pre-Algebra : Distributive Property

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #1 : Distributive Property

Simplify the expression.

\displaystyle (-2)(x^2+x-8)

Possible Answers:

\displaystyle -2x^2-2x+16

\displaystyle 2x^2+2x+16

\displaystyle 2x^2+2x-16

\displaystyle -2x^2-2x-16

Correct answer:

\displaystyle -2x^2-2x+16

Explanation:

Use the distributive property to multiply each term of the polynomial by \displaystyle \small -2. Be careful to distribute the negative as well.

\displaystyle (-2)(x^2)+(-2)(x)-(-2)(8)

\displaystyle (-2x^2)+(-2x)-(-16)

\displaystyle -2x^2-2x+16

Example Question #2 : Distributive Property

Find the value of \displaystyle 2(3-2) -4(2+5-7).

Possible Answers:

-6

6

4

-2

2

Correct answer:

2

Explanation:

We can seperate the problem into two steps:

\displaystyle 2(3-2) = 2(1)=2

\displaystyle -4(2+5-7) = -4(0)=0

We then combine the two parts:

\displaystyle 2+0=2

 

Example Question #3 : Distributive Property

Distribute \displaystyle -4(5x+15y-9).

Possible Answers:

\displaystyle 20x-60y+36

\displaystyle -20x-60y-36

\displaystyle 20x+60y-36

\displaystyle -20x-60y+36

Correct answer:

\displaystyle -20x-60y+36

Explanation:

When distributing with negative numbers we must remember to distribute the negative to all of the variables in the parentheses.

Distribute the \displaystyle -4 through the parentheses by multiplying it with each object in the parentheses to get \displaystyle ((-4)5x+(-4)15y-(-4)9).

Perform the multiplication remembering the positive/negative rules to get \displaystyle -20x-60y+36, our answer.

Example Question #4 : Distributive Property

Simplify the expression.

\displaystyle (-x+2)(-xy)

Possible Answers:

\displaystyle -2x^3y^2

\displaystyle x^2y-2xy

\displaystyle -x^2y-2xy

\displaystyle 2x^3y^2

Correct answer:

\displaystyle x^2y-2xy

Explanation:

Multiply the mononomial by each term in the binomial, using the distributive property.

\displaystyle (-x+2)(-xy)

\displaystyle (-xy)(-x)+(-xy)(2)

\displaystyle x^2y+(-2xy)

\displaystyle x^2y-2xy

 

Example Question #5 : Distributive Property

Simplify the expression.

\displaystyle 2x(5+4x+y)

Possible Answers:

\displaystyle 10x+6x^2+2xy

\displaystyle 10+8x+2y

\displaystyle 10x+8x^2+2xy

\displaystyle 5+6x+y

\displaystyle 10x+8x^2+y

Correct answer:

\displaystyle 10x+8x^2+2xy

Explanation:

\displaystyle 2x(5+4x+y)

Use the distributive property to multiply each term by \displaystyle \small 2x.

\displaystyle 2x(5)+2x(4x)+2x(y)

Simplify.

\displaystyle 10x+8x^2+2xy

Example Question #6 : Distributive Property

Distribute:

\displaystyle -3(-4x+5y-8)

Possible Answers:

\displaystyle 12x+15y+24

\displaystyle 12x+15y-24

\displaystyle x-7y+24

\displaystyle 12x-15y+24

\displaystyle -12x+15y-24

Correct answer:

\displaystyle 12x-15y+24

Explanation:

When distributing with negative numbers we must remember to distribute the negative to all of the terms in the parentheses.

Remember, a negative multiplied by a negative is positive, and a negative multiplied by a positive number is negative.

Distribute the \displaystyle -3 through the parentheses:

\displaystyle -4x(-3)+5y(-3)-8(-3)

Perform the multiplication, remembering the positive/negative rules:

\displaystyle 12x-15y+24

 

Example Question #7 : Distributive Property

Which of the following is equivalent to \displaystyle -3(2d - 4)?

Possible Answers:

\displaystyle -6d + 4

\displaystyle -6d - 4

\displaystyle -6d + 12

\displaystyle -6d - 12

\displaystyle 6d - 12

Correct answer:

\displaystyle -6d + 12

Explanation:

We need to distribute -3 by multiplying both terms inside the parentheses by -3.:

 \displaystyle -3(2d - 4) = -3(2d) + (-3)(-4).

Now we can multiply and simplify. Remember that multiplying two negative numbers results in a positive number:

\displaystyle -3(2d)+(-3)(-4)= -6d + 12

Example Question #8 : Distributive Property

Expand:

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

Possible Answers:

\displaystyle 12x^3+28x-8x

\displaystyle -12x^3+28x^{2}-8x

\displaystyle 12x^3-28x+8x

\displaystyle -12x^3-28x-8x

\displaystyle 12x^3+28x-8

Correct answer:

\displaystyle -12x^3+28x^{2}-8x

Explanation:

\displaystyle \small -4x(3x^2-7x+2)

Use the distributive property. Do not forget that the negative sign needs to be distributed as well!

\displaystyle \small \small (-4x)(3x^2)=-12x^3

\displaystyle \small (-4x)(-7x)=28x^2

\displaystyle \small (-4x)(2)=-8x

Add the terms together:

\displaystyle \small -12x^3+28x^2+(-8x)=-12x^3+28x^2-8x

Example Question #1 : Distributive Property

Distribute:

\displaystyle -5(x+15)

Possible Answers:

\displaystyle -5x-15

\displaystyle 5x+75

\displaystyle -5x-75

\displaystyle -5x+75

\displaystyle -5x+15

Correct answer:

\displaystyle -5x-75

Explanation:

Remember that a negative multiplied by a negative is positive, and a negative multiplied by a positive is negative.

Distribute the \displaystyle -5 through the parentheses by multiplying it by each of the two terms: 

\displaystyle -5x-75

 

Example Question #2 : Distributive Property

Expand:

\displaystyle 5(2+y)

Possible Answers:

\displaystyle 10 +y

\displaystyle 10 + 5y

\displaystyle 10y

\displaystyle 10y

\displaystyle 2y+5

Correct answer:

\displaystyle 10 + 5y

Explanation:

Distribute the \displaystyle 5 by multiplying it by each term inside the parentheses. 

\displaystyle 5\cdot 2=10 

and

\displaystyle 5\cdot y=5y

Therefore, 5(2 + y) = 10 + 5y.

 

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