How to Multiply Binomials

How to Multiply Binomials

Binomials are the sum or difference of two terms in an algebraic expression. Here you learn how to multiply them using FOIL method.

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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): \((x+3)(x-2)=x^2−2x+3x−6 \)
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):
\((x-4)(x-2)=x^2-2x-4x+8 \)
Then simplify: \(x^2-6x+8\)

Multiplying Binomials – Example 3:

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

Solution:

Use “FOIL”. (First–Out–In–Last):
\( (x-2)(x+2)=x^2+2x-2x-4 \)
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):
\((x+5)(x-2)=x^2-2x+5x-10 \)
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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