Algebra 1 : How to multiply a monomial by a polynomial

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : How To Multiply A Monomial By A Polynomial

 

Possible Answers:

Correct answer:

Explanation:

 

 

Example Question #422 : Variables

Evaluate.

Possible Answers:

Correct answer:

Explanation:

Using the distributive property you are simply going to share the term , with every term in the poynomial

Now because we are multiplying like variables we can add the exponents, to simplify each expression

   

This will be our final answer because we can not add terms unless they are 'like' meaning they contain the same elements and degrees. 

 

 

Example Question #423 : Variables

Multiply:

Possible Answers:

Correct answer:

Explanation:

Example Question #424 : Variables

Simplify the following:

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Distribute the  to each term in the parentheses in the other polynomial.

Putting the results back together

Example Question #1 : How To Multiply A Monomial By A Polynomial

Multiply:

Possible Answers:

Correct answer:

Explanation:

Multiply each term of the polynomial by . Be careful to distribute the negative sign.

 

Add the individual terms together:

Example Question #426 : Variables

Simplify the following

Possible Answers:

Correct answer:

Explanation:

Distribute  to each term in the parentheses in the polynomial

Combine the results

Example Question #6 : Monomials

Expand the expression by multiplying the terms.

Possible Answers:

Correct answer:

Explanation:

When multiplying, the order in which you multiply does not matter. Let's start with the first two monomials.

 

Use FOIL to expand.

Now we need to multiply the third monomial.

Similar to FOIL, we need to multiply each combination of terms.

Combine like terms.

Example Question #4 : Simplifying Expressions

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 #8 : Simplifying Expressions

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 #2 : How To Multiply A Monomial By A Polynomial

Write  as a polynomial. 

Possible Answers:

Correct answer:

Explanation:

We need to distribute the 4x2 through the terms in the parentheses:

This becomes .

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