←
Multiply Binomials: Mini-Lesson Review

Multiply Binomials: Mini-Lesson Review

Multiply Binomials: Mini-Lesson Review

Mini Lesson Question

Question #1: Multiply Binomials

Multiply the binomials.

( 3 x + 1 ) ( 2 x − 4 )

  1. 6 x 2 − 12 x − 4
  2. 6 x 2 + 2 x − 4
  3. 6 x 2 + 10 x − 4
  4. 6 x 2 − 10 x − 4

Multiplying Binomials

You can multiply polynomials using the distributive property.

Example 1

Multiply ( x + 3 ) ( x + 7 ) ( x + 3 ) ( x + 7 ) using the distributive property.

Step 1 - Multiply each term in the first binomial by the second binomial.

( x + 3 ) ( x + 7 ) ( x + 3 ) ( x + 7 )

x ( x + 7 ) + 3 ( x + 7 ) x ( x + 7 ) + 3 ( x + 7 )

Step 2 - Use the distributive property to eliminate the parentheses.

x 2 + 7 x + 3 x + 21 x 2 + 7 x + 3 x + 21

Step 3 - Combine like terms.

x 2 + 10 x + 21 x 2 + 10 x + 21

There is a pattern when multiplying two polynomials that are binomials.

  • The first term in the result is the product of the first terms in each binomial.
  • The second and third terms are the product of multiplying the two outer terms and then the two inner terms.
  • The last term results from multiplying the two last terms.

The method “First, Outer, Inner, Last” is abreviated as FOIL. It represents multiplying the First terms, Last terms, Inner terms, and Last terms of the binomials. The word “FOIL” is easy to remember and ensures you find all four products.

Example 2

Multiply ( x + 3 ) ( x + 7 ) ( x + 3 ) ( x + 7 ) using FOIL.

Step 1 - Multiply the First terms, Outer terms, Inner terms, and Last terms.

Image explaining how the acronym FOIL applies to the multiplication of two binomials. An arrow above labeled F goes from x in one binomial to x in the other binomial. An arrow below labeled O goes from x in the first binomial to 7 in the second binomial. An arrow below labeled I goes from 3 in the first binomial to x in the second binomial. And, an arrow above labeled L goes from 3 in the first binomial to 7 in the second binomial.

x 2 + 7 x + 3 x + 21 x 2 + 7 x + 3 x + 21

Step 2 - Combine like terms.

x 2 + 10 x + 21 x 2 + 10 x + 21

Example 3

Multiply ( x − 3 ) ( 2 x + 7 ) ( x − 3 ) ( 2 x + 7 ) using FOIL.

Step 1 - Multiply the First terms, Outer terms, Inner terms, and Last terms.

2 x 2 + 7 x − 6 x − 21 2 x 2 + 7 x − 6 x − 21

Step 2 - Combine like terms.

2 x 2 + x − 21 2 x 2 + x − 21

Try it

Multiplying Binomials

Multiply ( 7 x + 1 ) ( 2 x − 3 ) ( 7 x + 1 ) ( 2 x − 3 ) using FOIL.

Here is how to multiply (7x+1)(2x-3) using FOIL.

Step 1 - Multiply the First terms, Outer terms, Inner terms, and Last terms.

14 x ^ 2 − 21 x + 2 x − 3 14 x ^ 2 − 21 x + 2 x − 3

Step 2 - Combine like terms.

14 x ^ 2 − 19 x − 3 14 x ^ 2 − 19 x − 3

Check Your Understanding

Multiply the binomials.

( 2 x + 5 ) ( 3 x − 2 ) ( 2 x + 5 ) ( 3 x − 2 )

  1. 6 x 2 + 11 x − 10 6 x 2 + 11 x − 10

  2. 6 x 2 − 11 x − 10 6 x 2 − 11 x − 10

  3. 6 x 2 + 15 x − 10 6 x 2 + 15 x − 10

  4. 6 x 2 + 19 x − 10 6 x 2 + 19 x − 10

6 x 2 + 11 x − 10 6 x 2 + 11 x − 10

  • The first term in the result is the product of the first terms in each binomial.
     ( 2 x ) ( 3 x ) = 6 x 2 ( 2 x ) ( 3 x ) = 6 x 2
  • The second and third terms are the product of multiplying the two outer terms and then the two inner terms. Outer terms ( 2 x ) ( − 2 ) = − 4 x ( 2 x ) ( − 2 ) = − 4 x ; Inner terms ( 5 ) ( 3 x ) = 15 x ( 5 ) ( 3 x ) = 15 x
  • The last term results from multiplying the two last terms. ( 5 ) ( − 2 ) = − 10 ( 5 ) ( − 2 ) = − 10
  • So, 6 x 2 − 4 x + 15 x − 10 = 6 x 2 + 11 x − 10 6 x 2 − 4 x + 15 x − 10 = 6 x 2 + 11 x − 10

Video: Multiplying Binomials

Watch the following video to learn more about multiplying binomials.

Khan Academy: Multiplying Binomials

Access multimedia content