FOIL Calculator

Multiply two binomials, combine like terms, and see each First, Outer, Inner, and Last product clearly.

Quick Answer

For (x + 3)(x + 5), FOIL gives First: x², Outer: 5x, Inner: 3x, Last: 15. Combine like terms to get x² + 8x + 15.

(ax + b)(cx + d)

First binomial: ax + b

Second binomial: cx + d

Use positive, negative, decimal, or fractional decimal coefficients. Example: a=2, b=-1, c=1, d=4 means (2x – 1)(x + 4).

Expanded result
x² + 8x + 15

(x + 3)(x + 5) expanded and simplified.

x² coefficient1
x coefficient8
constant15
Steps

  1. First: x · x = x².
  2. Outer: x · 5 = 5x.
  3. Inner: 3 · x = 3x.
  4. Last: 3 · 5 = 15.
  5. Combine like terms: x² + 8x + 15.

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How to Use the FOIL Calculator

Enter the four coefficients for two binomials in the form ax + b and cx + d. The calculator multiplies the terms, adds the two x terms, and returns the simplified quadratic.

  1. Enter a and b for the first binomial.
  2. Enter c and d for the second binomial.
  3. Review the First, Outer, Inner, and Last steps.

FOIL Formula

FOIL is a shortcut for multiplying two binomials. It works because each term in the first binomial must multiply each term in the second binomial.

(ax + b)(cx + d) = acx² + adx + bcx + bd = acx² + (ad + bc)x + bd

FOIL Examples

Basic example

(x + 3)(x + 5) expands to x² + 8x + 15.

Leading coefficient example

(2x – 1)(x + 4) expands to 2x² + 7x – 4.

Negative leading term

(-x + 2)(3x – 5) expands to -3x² + 11x – 10.

How FOIL Connects to Factoring

FOIL expands factored binomials into a polynomial. Factoring moves in the reverse direction: it tries to turn a polynomial such as x² + 8x + 15 back into (x + 3)(x + 5).

Use FOIL to check a factorization result, verify homework steps, or prepare a quadratic expression for graphing.

Common FOIL Mistakes

Forgetting to combine the outer and inner terms

The middle term is adx + bcx. Add those coefficients before writing the final answer.

Dropping a negative sign

Negative constants and negative leading coefficients change both the x term and the constant term. Keep signs attached to their numbers.

Using FOIL for more than two binomials

FOIL is designed for two binomials. For three factors, multiply two binomials first, then multiply the result by the third factor.

FOIL Calculator FAQs

What does FOIL stand for?

FOIL stands for First, Outer, Inner, Last. It names the four products used when multiplying two binomials.

Can I use decimals?

Yes. Enter decimal coefficients such as 0.5 or -2.25.

Can this factor a quadratic?

This page expands binomials. Use the factoring calculator to go from an expanded polynomial back to factors.

Does the order of the binomials matter?

No. Multiplication is commutative, so reversing the two binomials gives the same expanded result.

Related SolverCalc tools

Factoring CalculatorReverse FOIL and factor polynomials.Simplify CalculatorCombine like terms after expanding.Graphing CalculatorPlot the expanded quadratic.

Reviewer

This educational math content is reviewed under the SolverCalc reviewer rule by Prof. Dr. Khalil Mudassar. WordPress adds the author bio automatically, so this page does not include a duplicate author box.

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Disclaimer

This calculator is intended for general educational and practical algebra use. Check signs and coefficients before using answers in graded work.