# Algebra II : Simplifying Expressions

## Example Questions

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### Example Question #1 : Simplifying Expressions

Simplify x(4 – x) – x(3 – x).

Possible Answers:

3x

1

0

x

x2

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 : How To Divide Trinomials

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 #1 : 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 #1 : Simplifying Expressions

Simplify the following: Possible Answers:     Correct answer: Explanation: First, let us factor the numerator:  ### Example Question #8 : Monomials

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 #3 : 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 #9 : Monomials

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 : Binomials

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). ← Previous 1 3 4 5 6 7 8

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