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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : High School Math

Distribute:

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

Possible Answers:

12x+15y+24

12x+15y-24

-12x+15y-24

x-7y+24

12x-15y+24

Correct answer:

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 through the parentheses:

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

Perform the multiplication, remembering the positive/negative rules:

12x-15y+24

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Example Question #1411 : Pre Algebra

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

Possible Answers:

-6d + 4

6d - 12

-6d - 12

-6d + 12

-6d - 4

Correct answer:

-6d + 12

Explanation:

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

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

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

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

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Example Question #5 : High School Math

Expand:

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

Possible Answers:

12x^3-28x+8x

$-12x^3+28x^{2}-8x$

12x^3+28x-8

12x^3+28x-8x

-12x^3-28x-8x

Correct answer:

$-12x^3+28x^{2}-8x$

Explanation:

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

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

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

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

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

Add the terms together:

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

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Example Question #11 : High School Math

Distribute:

-5(x+15)

Possible Answers:

-5x-75

-5x+15

-5x+75

5x+75

-5x-15

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 #1 : Distributive Property

Expand:

5(2+y)

Possible Answers:

2y+5

10y

10 +y

10y

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 #1412 : Pre Algebra

Simplify the expression:

(x+2)(-2)

Possible Answers:

x+4

-2x-4

-2x+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:

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

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

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

$\small 6x^8y^4$

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 #1413 : Pre Algebra

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

Possible Answers:

3x^2 - 4

5x-4

6x-2

6x-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 #1414 : Pre Algebra

Simplify the following expression:

8(5x-2)

Possible Answers:

=40x-16

=40x-2

=24x

=24

=5x-16

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 #1415 : Pre Algebra

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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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #3 : High School Math

Example Question #1411 : Pre Algebra

Example Question #5 : High School Math

Example Question #11 : High School Math

Example Question #1 : Distributive Property

Example Question #1412 : Pre Algebra

Example Question #11 : Distributive Property

Example Question #1413 : Pre Algebra

Example Question #1414 : Pre Algebra

Example Question #1415 : Pre Algebra

All Pre-Algebra Resources

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