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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

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 $\small -2$ $\displaystyle \small -2$ . Be careful to distribute the negative as well.

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

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

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

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Example Question #391 : Operations And Properties

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

Possible Answers:

-6

-2

Correct answer:

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:

2+0=2 $\displaystyle 2+0=2$

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Example Question #2 : 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.

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Example Question #3 : Distributive Property

Simplify the expression.

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

Possible Answers:

$\displaystyle -2x^3y^2$

$\displaystyle -x^2y-2xy$

$\displaystyle x^2y-2xy$

2x^3y^2 $\displaystyle 2x^3y^2$

Correct answer:

$\displaystyle x^2y-2xy$

Explanation:

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

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

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

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

$\displaystyle x^2y-2xy$

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Example Question #392 : Operations And Properties

Simplify the expression.

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

Possible Answers:

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

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

$\displaystyle 10x+8x^2+y$

5+6x+y $\displaystyle 5+6x+y$

$\displaystyle 10+8x+2y$

Correct answer:

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

Explanation:

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

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

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

Simplify.

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

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Example Question #1 : High School Math

Simplify the following expression:

$\displaystyle 5(x + 2)$

Possible Answers:

5x -2 $\displaystyle 5x -2$

5x + 10 $\displaystyle 5x + 10$

x + 7 $\displaystyle x + 7$

5x + 2 $\displaystyle 5x + 2$

$\displaystyle 5x$

Correct answer:

5x + 10 $\displaystyle 5x + 10$

Explanation:

Recall that the distributive property requires that we multiply the outside term by both terms in parentheses and add the results.

$5(x+2) = 5\cdot x + 5\cdot2 = 5x + 10$ $\displaystyle 5(x+2) = 5\cdot x + 5\cdot2 = 5x + 10$

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Example Question #3 : Whole Numbers

Evaluate the following expression:

$\displaystyle -2(3x + 4)$

Possible Answers:

None of the above

-5x + 4 $\displaystyle -5x + 4$

-6x + 4 $\displaystyle -6x + 4$

-6x - 8 $\displaystyle -6x - 8$

3x + 2 $\displaystyle 3x + 2$

Correct answer:

-6x - 8 $\displaystyle -6x - 8$

Explanation:

Recall the distributive property. We need to multiply the outside factor by both terms inside and then combine.

Thus,

$\displaystyle -2(3x + 4) = -2(3x) + (-2)(4) = -6x + (-8) = -6x - 8$

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Example Question #4 : Distributive Property

Distribute:

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

Possible Answers:

$\displaystyle 12x+15y+24$

$\displaystyle -12x+15y-24$

$\displaystyle 12x+15y-24$

x-7y+24 $\displaystyle x-7y+24$

$\displaystyle 12x-15y+24$

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:

$\displaystyle 12x-15y+24$

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Example Question #5 : Distributive Property

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

Possible Answers:

$\displaystyle -6d + 12$

$\displaystyle -6d - 12$

-6d - 4 $\displaystyle -6d - 4$

6d - 12 $\displaystyle 6d - 12$

-6d + 4 $\displaystyle -6d + 4$

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:

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

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Example Question #6 : Distributive Property

Expand:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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

Add the terms together:

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

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All High School Math Resources

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Distributive Property

Example Question #391 : Operations And Properties

Example Question #2 : Distributive Property

Example Question #3 : Distributive Property

Example Question #392 : Operations And Properties

Example Question #1 : High School Math

Example Question #3 : Whole Numbers

Example Question #4 : Distributive Property

Example Question #5 : Distributive Property

Example Question #6 : Distributive Property

All High School Math Resources

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