Algebra II : Simplifying Expressions

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #3 : How To Add Polynomials

Simplify x(4 – x) – x(3 – x).

Possible Answers:

0

x2

1

x

3x

Correct answer:

x

Explanation:

You must multiply out the first set of parenthesis (distribute) and you get 4x – x2. Then multiply out the second set and you get –3x + x2. Combine like terms and you get x.

x(4 – x) – x(3 – x)

4x – x2 – x(3 – x)

4x – x2 – (3x – x2)

4x – x2 – 3x + x2 = x

Example Question #1 : Simplifying Expressions

Divide:

Possible Answers:

Correct answer:

Explanation:

Factor the numerator and denominator:

Cancel the factors that appear in both the numerator and the denominator:

Example Question #2 : Simplifying Expressions

Simplify:        

Possible Answers:

Correct answer:

Explanation:

 and  cancel out, leaving  in the numerator. 5 and 25 cancel out, leaving 5 in the denominator

Example Question #3 : Simplifying Expressions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

First, let us factor the numerator:

Example Question #7 : How To Multiply A Monomial By A Polynomial

Find the product:

Possible Answers:

Correct answer:

Explanation:

First, mulitply the mononomial by the first term of the polynomial:

Second, multiply the monomial by the second term of the polynomial:

Add the terms together:

Example Question #4 : Simplifying Expressions

Multiply, expressing the product in simplest form:

Possible Answers:

Correct answer:

Explanation:

Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:

 

Now use the quotient rule on the variables by subtracting exponents:

Example Question #5 : Simplifying Expressions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

In this problem, you have two fractions being multiplied. You can first simplify the coefficients in the numerators and denominators. You can divide and cancel the 2 and 14 each by 2, and the 3 and 15 each by 3:

You can multiply the two numerators and two denominators, keeping in mind that when multiplying like variables with exponents, you simplify by adding the exponents together:

Any variables that are both in the numerator and denominator can be simplified by subtracting the numerator's exponent by the denominator's exponent. If you end up with a negative exponent in the numerator, you can move the variable to the denominator to keep the exponent positive:

Example Question #2 : How To Factor A Variable

Factor the expression:

Possible Answers:

Correct answer:

Explanation:

To find the greatest common factor, we need to break each term into its prime factors:

Looking at which terms all three expressions have in common; thus, the GCF is . We then factor this out: 

Example Question #8 : How To Multiply A Monomial By A Polynomial

Expand:

 

Possible Answers:

Correct answer:

Explanation:

To expand, multiply 8x by both terms in the expression (3x + 7).

8x multiplied by 3x is 24x².

8x multiplied by 7 is 56x.

Therefore, 8x(3x + 7) = 24x² + 56x.

Example Question #1 : How To Multiply Binomials With The Distributive Property

Simplify:

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

First, distribute –5 through the parentheses by multiplying both terms by –5.

Then, combine the like-termed variables (–5x and –3x).

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