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FOIL Method Calculator.

Expand (a x + b)(c x + d) using First, Outer, Inner, Last products.

On-device calculationNo signup
01

Set your values

Results update as you type.

First: 8

First

0.000000
Outer: 10

Outer

0.000000
Inner: 12

Inner

0.000000
Last: 15

Last

0.000000
x² coefficient: 8

x² coefficient

0.000000
x coefficient: 22

x coefficient

0.000000
Constant: 15

Constant

0.000000

Results update automatically as you type.

Use Cases

Check your algebra homework

Quickly verify the expansion of binomial products you've done by hand. Enter the coefficients and compare the result with your work.

Example: For (2x + 3)(x - 5), enter a=2, b=3, c=1, d=-5 to get 2x² - 7x - 15.

Simplify expressions for calculus or physics

When you need to expand binomials as part of a larger problem, use this tool to avoid arithmetic errors and save time.

Example: Expand (3x + 2)(4x - 1) to get 12x² + 5x - 2.

Frequently Asked Questions

What is the FOIL method?
FOIL stands for First, Outer, Inner, Last. It's a technique to multiply two binomials like (ax + b)(cx + d). You multiply the first terms (a and c), then the outer terms (a and d), inner terms (b and c), and last terms (b and d), then combine like terms.
How do I use this calculator?
Enter the coefficients a, b, c, and d from your binomials (ax + b) and (cx + d). The calculator will compute the products and show the expanded form, typically as acx² + (ad + bc)x + bd.
Can I use negative numbers for a, b, c, or d?
Yes, you can enter negative numbers. The calculator handles them correctly, and the expanded form will include the appropriate signs.

Tips & Common Mistakes

Tips

  • Double-check that you've entered the coefficients in the correct order: a and b for the first binomial, c and d for the second.
  • If a coefficient is 1, you can enter 1; if it's -1, enter -1. The calculator will handle it.
  • Use the result to practice the FOIL method manually: multiply First, Outer, Inner, Last, then combine like terms.
  • Remember that the FOIL method only works for multiplying two binomials. For other polynomials, use distribution.

Common Mistakes to Avoid

  • Mixing up the order of coefficients: ensure a and b are from the first binomial, c and d from the second.
  • Forgetting to combine like terms: the calculator does this for you, but when doing it manually, don't forget to add ad and bc.
  • Entering a negative sign incorrectly: if a term is negative, include the minus sign in the coefficient field.

Last updated: August 13, 2026