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GED Math : Simplifying, Distributing, and Factoring

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Example Questions

Example Question #41 : Algebra

A triangle has a base of x-2 ft and height of 2x+2 ft. What is the area (in square feet) of the triangle?

Possible Answers:

$2x^{2}-2x-4$

$2x^{2}+2x-4$

x^2-x-2

Correct answer:

x^2-x-2

Explanation:

The area of a triangle is: $A= \frac{1}{2}bh$

Use the FOIL Method to simplify.

$=\frac{1}{2} (x-2)(2x+2)$

$= \frac{1}{2}((x)(2x)) + (x)(2)+ (-2)(2x)-4)$

$= \frac{1}{2}(2x^2+2x-4x-4)$

$= \frac{1}{2}(2x^2-2x-4)$

A = x^2 - x -2

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Example Question #41 : Simplifying, Distributing, And Factoring

Simplify

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

Possible Answers:

x - 32

9x - 8

9x - 32

x - 8

Correct answer:

x - 32

Explanation:

The first step is to distribute the number outside of the parenthesis to the values inside the parenthesis.

(5x - 20) - (4x + 12)

Then in order to simplify you would combine like terms.

5x - 4x = x .

-20 - 12 = -32

x - 32

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Example Question #43 : Algebra

Solve: 3(x+5) = -2(5x+3)

Possible Answers:

$-\frac{21}{13}$

$\textup{The answer is not given.}$

$-\frac{9}{13}$

$\frac{9}{13}$

$\frac{7}{9}$

Correct answer:

$-\frac{21}{13}$

Explanation:

Distribute the terms on both sides.

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

3x+15 = -10x-6

Add 10x on both sides.

3x+15 +10x= -10x-6+10x

13x+15 = -6

Subtract 15 on both sides.

13x+15 -15= -6-15

13x =-21

Divide by 13 on both sides.

$\frac{13x}{13} =\frac{-21}{13}$

The answer is: $-\frac{21}{13}$

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Example Question #593 : Ged Math

Solve: 3x+7 = -19(-2x)

Possible Answers:

$-\frac{26}{5}$

$-\frac{1}{5}$

$\frac{1}{5}$

$\frac{7}{18}$

Correct answer:

$\frac{1}{5}$

Explanation:

Simplify the right side.

3x+7 =38x

Subtract on both sides.

3x+7-3x =38x-3x

7= 35x

Divide both sides by 35.

$\frac{7}{35}=\frac{ 35x}{35}$

The answer is: $\frac{1}{5}$

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Example Question #41 : Algebra

Simplify by distributing:

-7 (3x + 8y - 7z )

Possible Answers:

-21 x +56y-49z

-21 x -56y+49z

-21 x -56y-49z

-21 x +56y+49z

Correct answer:

-21 x -56y+49z

Explanation:

Using the Distributive Property of Multiplication over Addition, multiply by each of the terms between the parentheses:

-7 (3x + 8y - 7z )

$=(-7 ) \cdot 3x +(-7 ) \cdot 8y - (-7 ) \cdot 7z$

Multiply out each coefficient:

= -21 x +(-56)y - (-49)z

Simplify the addition and subtraction of the resulting negatives in the second and third terms:

= -21 x -56y+49z

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Example Question #42 : Single Variable Algebra

Simplify the following equation: 8x-24 = 12

Possible Answers:

$\frac{3}{2}$

$\frac{9}{2}$

$\frac{2}{3}$

$\frac{2}{9}$

Correct answer:

$\frac{9}{2}$

Explanation:

Add 24 on both sides of the equation.

8x-24 +24= 12+24

8x=36

Divide by 8 on both sides.

$\frac{8x}{8}=\frac{36}{8}$

Reduce both fractions.

$\frac{36}{8} = \frac{4\times 9}{4\times 2}$

The answer is: $\frac{9}{2}$

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Example Question #41 : Simplifying, Distributing, And Factoring

Factor: 3x^3 -3x^2-9x^5

Possible Answers:

-3x^2(-3x^3-x-1)

3x^2(-3x^3-x-1)

-3x(3x^3-x-1)

3x^2(-3x^3+x-1)

-3x^2(3x^3-x-1)

Correct answer:

3x^2(-3x^3+x-1)

Explanation:

In order to factor, we will need to pull out a term that all terms share.

3x^3 -3x^2-9x^5 = 3x^2(x-1-3x^3)

The answer is: 3x^2(-3x^3+x-1)

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Example Question #41 : Single Variable Algebra

Simplify: $3x^2(\frac{1}{6x}-\frac{1}{2})$

Possible Answers:

$\frac{1}{2}- \frac{3}{2}x^2$

$\frac{1}{2}x- \frac{3}{2}x^2$

$\frac{1}{2x^3}- \frac{1}{6x^2}$

$\frac{1}{2x^3}- \frac{3}{2}$

-x^2

Correct answer:

$\frac{1}{2}x- \frac{3}{2}x^2$

Explanation:

Distribute the outer term through both of the inner terms.

$3x^2(\frac{1}{6x}-\frac{1}{2}) = 3x^2(\frac{1}{6x}) -3x^2(\frac{1}{2})$

Simplify the terms.

The answer is: $\frac{1}{2}x- \frac{3}{2}x^2$

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Example Question #42 : Algebra

Solve the equation: $\frac{3}{x}= -7$

Possible Answers:

$-\frac{7}{3}$

$-\frac{1}{21}$

$-\frac{3}{7}$

$-\frac{1}{10}$

Correct answer:

$-\frac{3}{7}$

Explanation:

Multiply both sides by .

$\frac{3}{x} \cdot x= -7\cdot x$

3 = -7x

Divide by negative seven on both sides.

$\frac{3}{-7} = \frac{-7x}{-7}$

The answer is: $-\frac{3}{7}$

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Example Question #41 : Simplifying, Distributing, And Factoring

Simplify the following fraction:

$\frac{x^3+4x^2-24x}{x^3-2x^2-3x}$

Possible Answers:

$\frac{x-3}{x+8}$

$\frac{x+3}{x-1}$

$\frac{x+8}{x}$

$\frac{x+8}{x+1}$

Correct answer:

$\frac{x+8}{x+1}$

Explanation:

$\frac{x^3+4x^2-24x}{x^3-2x^2-3x}$

Start by factoring the numerator.

Notice that each term in the numerator has an , so we can factor that out.

x^3+4x^2-24x=x(x^2+5x-24)

Now, factor the expression within the parentheses.

x(x^2+5x-24)=x(x+8)(x-3)

Now, factor the denominator. Notice that each term in the denominator also has an , so we can factor that out too.

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

Next, factor the expression within the parentheses.

x(x^2-2x-3)=x(x-3)(x+1)

Rewrite the fraction using the factored forms of both numerator and denominator.

$\frac{x^3+4x^2-24x}{x^3-2x^2-3x}=\frac{x(x+8)(x-3)}{x(x-3)(x+1)}$

Since the numerator and denominator both have the terms and x-3 , those will cancel out, leaving us with the following:

$\frac{x^3+4x^2-24x}{x^3-2x^2-3x}=\frac{x+8}{x+1}$

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GED Math : Simplifying, Distributing, and Factoring

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #41 : Algebra

Example Question #41 : Simplifying, Distributing, And Factoring

Example Question #43 : Algebra

Example Question #593 : Ged Math

Example Question #41 : Algebra

Example Question #42 : Single Variable Algebra

Example Question #41 : Simplifying, Distributing, And Factoring

Example Question #41 : Single Variable Algebra

Example Question #42 : Algebra

Example Question #41 : Simplifying, Distributing, And Factoring

All GED Math Resources

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