How to multiply a monomial by a polynomial - Algebra 1

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

This becomes .

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:

times gives us , while times 4 gives us . So it equals .

Be sure to distribute the along with its coefficient.

Use the distributive property to obtain each term:

Distribute the outside term into the parentheses.

Simplify each distributed factor into one expression.

Distribute the outside term into the parentheses.

Simplify each distributed factor into one expression.

Distribute and multiply by each of the terms within the parentheses.

Regroup the resulting terms

Distribute to each of the terms within the parentheses.

Putting it back together...

Distribute to each term within parentheses.

Putting it back together...

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.

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.

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

Putting the results back together

Distribute to each term in the parentheses in the polynomial

Combine the results

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

Add the individual terms together: