How to Multiply Binomials? (+FREE Worksheet!)
Binomials are the sum or difference of two terms in an algebraic expression. Here you learn how to multiply them using the FOIL method.
Related Topics
- How to Multiply Monomials
- How to Multiply and Dividing Monomials
- How to Multiply a Polynomial and a Monomial
- How to Factor Trinomials
- How to Add and Subtract Polynomials
Step-by-step guide to Multiplying Binomials
- The sum or the difference of two terms in an algebraic expression is a binomial.
- Use “FOIL” (First–Out–In–Last) to multiply Binomials.
(x+a)(x+b)=x2+(b+a)x+ab
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Multiplying Binomials – Example 1:
Multiply Binomials. (x+3)(x−2)=
Solution:
Use “FOIL”. (First–Out–In–Last):
(x+3)(x−2)=x2−2x+3x−6
Now combine like terms: −2x+3x=x
Then simplify: x2−2x+3x−6=x2+x−6
Multiplying Binomials – Example 2:
Multiply Binomials. (x−4)(x−2)=
Solution:
Use “FOIL”. (First–Out–In–Last):
(x−4)(x−2)=x2−2x−4x+8
Now combine like terms: −2x−4x=−6x
Then simplify: x2−2x−4x+8= x2−6x+8
Multiplying Binomials – Example 3:
Multiply Binomials. (x−2)(x+2)=
Solution:
Use “FOIL”. (First–Out–In–Last):
(x−2)(x+2)=x2+2x−2x−4
Now combine like terms: 2x−2x=0
Then simplify: x2+2x−2x−4=x2−4
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Multiplying Binomials – Example 4:
Multiply Binomials. (x+5)(x−2)=
Solution:
Use “FOIL”. (First–Out–In–Last):
(x+5)(x−2)=x2−2x+5x−10
Now combine like terms: −2x+5x=3x
Then simplify: x2−2x+5x−10=x2+3x−10
Exercises for Multiplying Binomials
Multiply.
- \color{blue}{ (3x – 2) (4x + 2)}
- \color{blue}{(2x – 5) (x + 7)}
- \color{blue}{ (x + 2) (x + 8)}
- \color{blue}{ (x^2 + 2) (x^2 – 2)}
- \color{blue}{ (x – 2) (x + 4)}
- \color{blue}{ (x – 8) (2x + 8)}
Download Multiplying Binomials Worksheet
- \color{blue}{12x^2 – 2x – 4 }
- \color{blue}{2x^2 + 9x – 35 }
- \color{blue}{ x^2 + 10x + 16}
- \color{blue}{x^4 – 4 }
- \color{blue}{x^2 + 2x – 8 }
- \color{blue}{2x^2 – 8x – 64 }
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