# Algebra 1 : How to multiply a monomial by a polynomial

## Example Questions

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Explanation:

### Example Question #2 : How To Multiply A Monomial By A Polynomial

Evaluate.

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.

Multiply:

Explanation:

### Example Question #4 : How To Multiply A Monomial By A Polynomial

Simplify the following:

Explanation:

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

Putting the results back together

### Example Question #1 : Monomials

Multiply:

Explanation:

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

### Example Question #6 : How To Multiply A Monomial By A Polynomial

Simplify the following

Explanation:

Distribute  to each term in the parentheses in the polynomial

Combine the results

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

Expand the expression by multiplying the terms.

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 #1 : Simplifying Expressions

Find the product:

Explanation:

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

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

### Example Question #2 : Monomials

Expand:

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 : Monomials

Write  as a polynomial.