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.

How to Multiply Binomials? (+FREE Worksheet!)

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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.
    \(\color{blue}{(x+a)(x+b)=x^2+(b+a)x+ab}\)

Multiplying Binomials – Example 1:

Multiply Binomials. \((x+3)(x-2)=\)

Solution:

Use “FOIL”. (First–Out–In–Last):

\((x+3)(x-2)=x^2−2x+3x−6 \)

Now combine like terms: \(-2x+3x=x\)
Then simplify: \(x^2−2x+3x−6=x^2+x−6\)

Multiplying Binomials – Example 2:

Multiply Binomials. \((x-4)(x-2)=\)

Solution:

Use “FOIL”. (First–Out–In–Last):
\((x-4)(x-2)=x^2-2x-4x+8 \)

Now combine like terms: \(-2x-4x=-6x\)
Then simplify: \(x^2-2x-4x+8 =\) \(x^2-6x+8\)

Multiplying Binomials – Example 3:

Multiply Binomials. \((x-2)(x+2)=\)

Solution:

Use “FOIL”. (First–Out–In–Last):
\( (x-2)(x+2)=x^2+2x-2x-4 \)

Now combine like terms: \(2x-2x=0\)
Then simplify: \(x^2+2x-2x-4=x^2-4\)

Multiplying Binomials – Example 4:

Multiply Binomials. \((x+5)(x-2)=\)

Solution:

Use “FOIL”. (First–Out–In–Last):
\((x+5)(x-2)=x^2-2x+5x-10 \)

Now combine like terms: \(-2x+5x=3x\)
Then simplify: \(x^2-2x+5x-10=x^2+3x-10\)

Exercises for Multiplying Binomials

Multiply.

  1. \(\color{blue}{ (3x – 2) (4x + 2)}\)
  2. \(\color{blue}{(2x – 5) (x + 7)}\)
  3. \(\color{blue}{ (x + 2) (x + 8)}\)
  4. \(\color{blue}{ (x^2 + 2) (x^2 – 2)}\)
  5. \(\color{blue}{ (x – 2) (x + 4)}\)
  6. \(\color{blue}{ (x – 8) (2x + 8)}\)

Download Multiplying Binomials Worksheet

  1. \(\color{blue}{12x^2 – 2x – 4 }\)
  2. \(\color{blue}{2x^2 + 9x – 35 }\)
  3. \(\color{blue}{ x^2 + 10x + 16}\)
  4. \(\color{blue}{x^4 – 4 }\)
  5. \(\color{blue}{x^2 + 2x – 8 }\)
  6. \(\color{blue}{2x^2 – 8x – 64 }\)

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