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Pre-Algebra : Identities and Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #4 : Distributive Property

Distribute:

-5(x+15)

Possible Answers:

-5x+75

-5x-75

-5x+15

-5x-15

5x+75

Correct answer:

-5x-75

Explanation:

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

Distribute the through the parentheses by multiplying it by each of the two terms:

-5x-75

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Example Question #5 : Distributive Property

Expand:

5(2+y)

Possible Answers:

10y

10 +y

2y+5

10 + 5y

Correct answer:

10 + 5y

Explanation:

Distribute the by multiplying it by each term inside the parentheses.

$5\cdot 2=10$

and

$5\cdot y=5y$

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

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Example Question #1 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Simplify the expression:

(x+2)(-2)

Possible Answers:

-2x+4

2x-4

x+4

2x+4

-2x-4

Correct answer:

-2x-4

Explanation:

To solve this question you must use the distrubitive property by multiplying x by -2 and the 2 by -2, making sure to distribute the negative as well. This gives you:

x(-2)+2(-2)

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Example Question #11 : Distributive Property

Simplify the expression:

$\small x^2y(3+2x+xy)$

Possible Answers:

$\small 3y+2xy+xy^2$

$\small 3x^2y+2x^3y+x^3y^2$

$\small 3x^2+2x^3+x^3y$

$\small 6x^8y^4$

Correct answer:

$\small 3x^2y+2x^3y+x^3y^2$

Explanation:

Recall the distributive property: $\small a(b+c+d) = (a*b)+(a*c)+(a*d)$

Therefore, we must multiply everything inside the parentheses by $\small x^2y$ .

$\small (3*x^2y)+(2x*x^2y)+(xy*x^2y)$

To simplify further, recall that multiplying like bases mean you add their exponents.

$\small \small 3x^2y+2x^{1+2}y+x^{1+2}y^{1+1}$

$\small 3x^2y+2x^3y+x^3y^2$

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Example Question #2 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Which answer correctly simplifies this expression? 2(3x-2)

Possible Answers:

6x-2

3x^2 - 4

6x-4

5x-4

Correct answer:

6x-4

Explanation:

To simplify this expression, use the distributive property. This means that we have to multiply the 2 times both terms inside the parentheses. 2*3x = 6x , and 2*-2 = -4 . So, our answer is 6x-4 .

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Example Question #1 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Simplify the following expression:

8(5x-2)

Possible Answers:

=24x

=24

=40x-16

=5x-16

=40x-2

Correct answer:

=40x-16

Explanation:

Apply the distributive property of multiplication to remove the parenthesis from the given expression. Multiply the term outside of the parenthesis to each of the terms inside the parenthesis.

8(5x-2)

=8*5x+8*(-2)

=40x-16

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Example Question #11 : Distributive Property

Which of the answers correctly shows the following equation distributed correctly?

2x(3x^2 + 5x - 9) =

Possible Answers:

(2x * 3x^2) + (2x * 5x) + (2x * -9)

(2x + 3x^2) * (2x + 5x) * (2x + -9)

2x * 3x^2 * 5x * -9

(2x + 3x^2) + (2x + 5x) + (2x + -9)

Correct answer:

(2x * 3x^2) + (2x * 5x) + (2x * -9)

Explanation:

2x(3x^2 + 5x -9) =

(2x*3x^2) + (2x * 5x) + (2x * -9)

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Example Question #15 : Distributive Property

Simplify: 2x(3+4x+3xy)

Possible Answers:

14x^2+6x^2y

6x+8x^2+6x^2y

14x+6x^2y

17x^2y

5x+6x^2+5x^2y

Correct answer:

6x+8x^2+6x^2y

Explanation:

Use the distributive property to simplify the expression.

This means multiply the with each term within the parentheses.

$\\2x(3+4x+3xy) \\$

= (2x)(3)+(2x)(4x)+(2x)(3xy)

= 6x+8x^2+6x^2y

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Example Question #12 : Distributive Property

Use the distributive property to evaluate: xy(xy+x+y^2)

Possible Answers:

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

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

2xy+2x+y+y^3

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

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

Correct answer:

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

Explanation:

Distribute throughout every term in the parentheses.

xy(xy+x+y^2)= (xy)(xy)+(xy)(x)+(xy)(y^2)

Simplify the terms.

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

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Example Question #12 : Distributive Property

Which of the following displays the distributive property?

Possible Answers:

$a \cdot b = ab$

(a + b)^2 = a^2 + 2ab + b^2

$a \cdot b = b \cdot a$

$(a \cdot b) \cdot c = a \cdot (b \cdot c)$

a(b + c) = ab + ac

Correct answer:

a(b + c) = ab + ac

Explanation:

The distributive property is defined as a way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multipled by a factor outside the parentheses. So,

a(b + c) = ab + ac

displays just that.

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Pre-Algebra : Identities and Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #4 : Distributive Property

Example Question #5 : Distributive Property

Example Question #1 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Example Question #11 : Distributive Property

Example Question #2 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Example Question #1 : Apply The Properties Of Operations To Generate Equivalent Expressions: Ccss.Math.Content.6.Ee.A.3

Example Question #11 : Distributive Property

Example Question #15 : Distributive Property

Example Question #12 : Distributive Property

Example Question #12 : Distributive Property

All Pre-Algebra Resources

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