High School Math : Simplifying Polynomials

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #1 : Simplifying Polynomials

Simplify the following expression: 

.

Possible Answers:

Correct answer:

Explanation:

First, multiply out the second expression so that you get .

Then, multiply your like terms, taking care to remember that when multiplying terms that have the same base, you add the exponents. Thus, you get .

Example Question #2 : Simplifying Polynomials

Simplify:

Possible Answers:

Correct answer:

Explanation:

Focus on each pair of like terms. The  completely cancel out, there is one  left on top, and five  left on the bottom. 

 reduces to .

Put that all together to get 

Example Question #3 : Simplifying Polynomials

Simplify.

Possible Answers:

Correct answer:

Explanation:

Put the negative exponent on the bottom so that you have  which simplifies further to .

Example Question #4 : Simplifying Polynomials

Expand this expression:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method (First, Outer, Inner, Last):

Put all of these terms together:

Combine like terms:

Example Question #5 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

To simplify the polynomial, begin by multiplying the first binomial by every term within the parentheses:

Now, combine like terms:

 

Convert the polynomial into fraction form:

Example Question #6 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

Now, combine like terms:

 

Simplify the integers:

Example Question #7 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Squaring the polynomial is equivalent to:

 

Use the FOIL method to multiply the terms:

F - First

O - Outer

I - Inner

L - Last

 

 

Combine like terms:

Example Question #1 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

Rearrange the terms once again so that the outer exponent is positive. Also, combine like terms:

 

Now, square the polynomial:

Example Question #9 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

To simplify the polynomial, begin by combining the terms within the parentheses and multiplying the integers:

 

 

Now, add together like terms:

Example Question #10 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

 

Now, combine like terms:

 

Simplify the integers:

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