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Algebra II : Simplifying Equations

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Example Question #11 : Simplifying Equations

Simplify:

$\frac{25x^{2}y^{3}}{20x^{2}y^{6}}$

Possible Answers:

$\frac{5y^{3}}{4y^{6}}$

$\frac{5}{4y^{3}}$

$\frac{5}{4y^{2}}$

$\frac{5y^{3}}{4}$

$\frac{4y^{3}}{5}$

Correct answer:

$\frac{5}{4y^{3}}$

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

5*5*x*x*y*y*y

The denominator can be factored to:

4*5*x*x*y*y*y*y*y*y

$\frac{5*5*x*x*y*y*y}{4*5*x*x*y*y*y*y*y*y}$

After reducing, we will get

$\frac{5}{4*y*y*y} = \frac{5}{4y^{3}}$

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Example Question #12 : Simplifying Equations

Simplify:

$\frac{4x^{2}}{2x}$

Possible Answers:

$\frac{4x}{2}$

Correct answer:

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

2*2*x*x

The denominator can be factored to:

2*x

$\frac{2*2*x*x}{2*x}$

After reducing, we will get

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Example Question #13 : Simplifying Equations

Solve for : $\frac{x(x^3+3y)}{x+2} = 2x$

Possible Answers:

$y=-\frac{1}{3}x^3-\frac{2}{3}x-\frac{4}{3}$

$y=\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

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

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

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

Correct answer:

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

Explanation:

Multiply x+2 on both sides in order to eliminate the denominator.

$\frac{x(x^3+3y)}{x+2} \cdot (x+2)= 2x\cdot (x+2)$

Simplify both sides.

x(x^3+3y) = 2x(x+2)

Use distribution to simplify both sides.

x^4+3xy = 2x^2+4x

Isolate the term with only the y-variable by subtracting x^4 on both sides.

x^4+3xy -x^4= 2x^2+4x-x^4

Simplify and reorder the right side by the order of power.

3xy = -x^4+2x^2+4x

Divide by on both sides.

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

Simplify both sides.

The answer is: $y=-\frac{1}{3}x^3+\frac{2}{3}x+\frac{4}{3}$

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Example Question #14 : Simplifying Equations

Simplify the equation: 6(2x-3)=-48

Possible Answers:

$-\frac{3}{2}$

$-\frac{2}{5}$

$-\frac{11}{2}$

$-\frac{5}{2}$

$-\frac{2}{11}$

Correct answer:

$-\frac{5}{2}$

Explanation:

In order to simplify and solve this equation, divide by six on both sides.

$\frac{6(2x-3)}{6}=\frac{-48}{6}$

Simplify both sides.

2x-3=-8

Add three on both sides.

2x-3+3=-8+3

Simplify both sides.

2x=-5

Divide both sides by two.

$\frac{2x}{2}=\frac{-5}{2}$

The answer is: $x=-\frac{5}{2}$

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Example Question #15 : Simplifying Equations

Simplify the following equation: 3x+9 = -57

Possible Answers:

Correct answer:

Explanation:

Subtract nine from both sides.

3x+9 -9= -57-9

3x=-66

Divide both sides.

$\frac{3x}{3}=\frac{-66}{3}$

x=-22

The answer is:

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Example Question #16 : Simplifying Equations

Simplify the equation: 2(3x-2) -38= 0

Possible Answers:

$-\frac{17}{3}$

$\frac{1}{7}$

$\frac{17}{3}$

Correct answer:

Explanation:

Add 38 on both sides.

2(3x-2) -38+38= 0+38

2(3x-2)=38

Divide by two on both sides.

$\frac{2(3x-2) }{2}= \frac{38}{2}$

The equation becomes:

3x-2 = 19

Add two on both sides.

3x-2 +2= 19+2

3x=21

Divide by three on both sides.

$\frac{3x}{3}=\frac{21}{3}$

The answer is:

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Example Question #17 : Simplifying Equations

Simplify the equation: $(\frac{2}{5}x)^2+\frac{1}{2}x-\frac{2}{5}x-8$

Possible Answers:

None of the other answers.

$\frac{4}{25}x^2-\frac{3}{7}x-8$

$\frac{4}{25}x+\frac{1}{10}x-8$

$\frac{2}{5}x^2+\frac{1}{10}x-8$

$\frac{4}{25}x^2+\frac{1}{10}x-8$

Correct answer:

$\frac{4}{25}x^2+\frac{1}{10}x-8$

Explanation:

$(\frac{2}{5}x)^2+\frac{1}{2}x-\frac{2}{5}x-8$

Start by squaring everything within the parentheses:

$\frac{4}{25}x^2+\frac{1}{2}x-\frac{2}{5}x-8$

Now combine the fractions of degree 1 by finding a common denominator:

$\frac{4}{25}x^2+\frac{5}{5}*\frac{1}{2}x-\frac{2}{2}*\frac{2}{5}x-8$

$\frac{4}{25}x^2+\frac{5}{10}x-\frac{4}{10}x-8\rightarrow \boldsymbol{\frac{4}{25}x^2+\frac{1}{10}x-8}$

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Example Question #11 : Simplifying Equations

Simplify this expression:

$(4x^{4}-x^{2})+(x^2+5x^4)$

Possible Answers:

3x^2-1

$9x^{4}$

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

$9x^{4}-2x^{2}$

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

Correct answer:

$9x^{4}$

Explanation:

Drop the parentheses and combine like terms.

$5x^{4}+4x^{4}=9x^{4}$

and

$-x^{2}+x^{2}=0$

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Example Question #19 : Simplifying Equations

Simplify the expression by combining like terms.

Simplify:

5x^2+15x+18 = 6x^2-8x+9

Possible Answers:

x^2+23x+9 = 0

5x^2-23x-9 = 6x^2

-x^2-23x+27 = 0

x^2-23x-9 = 0

11x^2-23x-9 = 0

Correct answer:

x^2-23x-9 = 0

Explanation:

The original equation:

5x^2+15x+18 = 6x^2-8x+9

Now move all terms to one side, in this example, we will use the right side, but either side will work.

0 = 6x^2 - 8x + 9 -5x^2 -15x-18

As you can see, we subtracted the terms on the left from both sides, effectively moving them to the other side.

Regrouping the terms so that "like terms" are together. Like terms are defined by having the same power of x.

0= (6x^2-5x^2)+(-8x-15x)+(9-18)

Now, we add any terms that have like powers of x.

x^2-23x-9 = 0

Now that all terms have been combined, we are finished. The equation is simplified.

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Algebra II : Simplifying Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Simplifying Equations

Example Question #12 : Simplifying Equations

Example Question #13 : Simplifying Equations

Example Question #14 : Simplifying Equations

Example Question #15 : Simplifying Equations

Example Question #16 : Simplifying Equations

Example Question #17 : Simplifying Equations

Example Question #11 : Simplifying Equations

Example Question #19 : Simplifying Equations

All Algebra II Resources

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