How to Use the FOIL Method
to Multiply Binomials

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Summary

How to Use the FOIL Method
to Multiply Binomials

  1. Multiply the FIRST terms of the binomials.
  2. Multiply the OUTER terms of the binomials.
  3. Multiply the INNER terms of the binomials.
  4. Multiply the LAST terms of the binomials.
  5. Combine like terms, if needed.

\(21x^2\) \(-28x\) \(-6x\) \(+8\)

\(21x^2-34x+8\)

Be sure to follow the rules for multiplying negative numbers when you multiply the coefficients of the terms. If you don't know how to multiply variables or how to combine like terms, check out the linked pages.

Example

\((3x-2)(-4x+5)\)

I'll start by multiplying the first terms of the binomials.

\((3x)(-4x)=-12x^2\)

Then I'll multiply the outer terms. 

\((3x)(5)=15x\)

Next, I'll multiply the inner terms.

\((-2)(-4x)=8x\)

Finally, I'll multiply the last terms.

\((-2)(5)=-10\)

So,

\((3x-2)(-4x+5)=-12x^2+15x+8x-10\)

Then I'll combine like terms (\(15x\) and \(8x\)) to simplify the answer.

\(15x+8x=23x\)

Answer:

\((3x-2)(-4x+5)=-12x^2+23x-10\)

Why It Works

Resources

Free Online Practice Problems

Khan Academy - Multiply Binomials


Free Printable Worksheets

MathWorksheets4Kids - Multiplying Binomials (Single Variable)

MathWorksheets4Kids - Multiplying Binomials (Multiple Variables)

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