Expanding expressions

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Some expressions use parentheses to show multiplication. When you expand an expression, you get rid of those parentheses!

You can use the

distributive property

to expand expressions. Multiply the term outside the parentheses by each term inside the parentheses. Then add those products.

Let's try it! Expand

(

)

(

)

Multiply 7 by each term inside the parentheses.

(

)

(

)

Multiply 7 by each term inside the parentheses.

So,

(

)

Try some practice problems!

Multiply using the distributive property

Expanding longer expressions

Sometimes, you will need to expand expressions with more than two terms inside of the parentheses. You can use the distributive property to expand these expressions, too. Be sure to multiply the term outside of the parentheses by each term inside of the parentheses.

Let's try it! Expand

(

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)

Notice the subtraction inside the parentheses. When you multiply

by each term, be sure to subtract the product of

and

(

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Multiply 2a by each term.

(

)

–

(

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(

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Multiply 2a by each term.

Simplify.

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Simplify.

So,

(

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)

–

Try some practice problems!

Multiply a polynomial by a monomial

Expanding more than once in the same expression

Sometimes, you will need to expand more than one set of parentheses in an expression. Expand each set of parentheses separately. Then,

combine like terms

if possible.

Let's try it! Expand

(

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)

(

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)

(

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)

(

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)

Apply the distributive property.

(

)

–

(

)

(

)

–

(

)

Apply the distributive property.

Simplify.

–

Simplify.

Combine like terms.

–

Combine like terms.

So,

(

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)

(

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)

–

Products of binomials

Some expressions are written as the product of two

binomials.

A binomial is an expression with two terms. For example, the expression

(

)

(

)

is written as the product of two binomials.

To multiply two binomials, multiply each term in the first binomial by each term in the second binomial. You can do this by using the FOIL method: find the products of the

First,

Outside,

Inside,

and

Last

terms, and then add those products.

Let's try it! Expand

(

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)

(

)

using the FOIL method.

It is easier to keep track of negative values if you rewrite subtraction as addition. Remember, subtracting a number is the same as adding its opposite. Let's rewrite the expression below.

(

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)

(

)

(

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)

(

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Now, apply the FOIL method.

Find the product of each pair of terms:

(

)

(

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–

(

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–

(

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Then, add those products and simplify.

–

Combine like terms.

–

Combine like terms.

Rewrite addition as subtraction.

–

Rewrite addition as subtraction.

So,

(

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)

(

)

–

Tip

The FOIL method is a helpful way to remember how to multiply two binomials. However, remember that the FOIL method only works for multiplying two binomials. For example, if you were to multiply two expressions with three terms each, you could not use the FOIL method.

Try some practice problems!

Multiply two binomials

Products of polynomials

An expression with two or more terms is called a

polynomial.

To expand an expression written as the product of two polynomials, you need to multiply each term in the first polynomial by each term in the second polynomial.

Let's try it! Expand

(

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)

(

–

)

(

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)

(

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)

Rewrite as addition.

(

–

)

(

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)

Rewrite as addition.

Apply the distributive property.

(

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)

–

(

–

)

Apply the distributive property.

(

)

(

–

)

(

)

–

(

)

–

(

–

)

–

(

)

Apply the distributive property.

Simplify.

–

Simplify.

Combine like terms.

–

Combine like terms.

Rewrite addition as subtraction.

–

Rewrite addition as subtraction.

So,

(

–

)

(

–

)

–

Try some practice problems!

Multiply polynomials

Skills

Multiply using the distributive property Multiply a polynomial by a monomial Multiply two binomials Multiply polynomials

Videos(4)

Multiply using the distributive property

Multiply a polynomial by a monomial

Multiply two binomials

Multiply polynomials

Lessons

Simplifying expressions

Factoring expressions

Try some practice problems!

Expanding longer expressions

Try some practice problems!

Expanding more than once in the same expression

Products of binomials

Try some practice problems!

Products of polynomials

Try some practice problems!

Related

Skills

Videos(4)

Lessons