FOIL Math Calculator

Here is how the calculator expands (x + 2)(x + 3):

1. First: x · x = x²
2. Outer: x · 3 = 3x
3. Inner: 2 · x = 2x
4. Last: 2 · 3 = 6
5. Combine: x² + 3x + 2x + 6
6. Simplify: x² + 5x + 6

The middle terms combine because 3x and 2x are like terms: same variable, same power. The x² term and the constant stay separate.

1. Enter the first binomial.
2. Enter the second binomial.
3. Check the signs, coefficients, and variables.
4. Select Calculate.
5. Review the First, Outer, Inner, and Last products.
6. See how the middle terms combine.
7. Check the simplified answer.
8. Select Reset for a new problem.

To verify by hand, substitute a number such as x = 1. For (x + 2)(x + 3), both 3 · 4 and 1 + 5 + 6 equal 12.

When both binomials start with x, the formula simplifies to:

The middle coefficient is the sum of the constants, and the last term is their product. x · x = x² because exponents add when you multiply the same variable.

For signs, keep each sign with its term: matching signs give a positive product, and different signs give a negative one. Write the answer in descending powers of x (x², then x, then the constant), called standard form.

Example 1 - FOIL With Positive Numbers

(x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6

Example 2 - FOIL With Negative Numbers

(x − 4)(x + 2) = x² + 2x − 4x − 8 = x² − 2x − 8

The −4 makes the Inner and Last products negative.

Example 3 - FOIL With Coefficients

(2x + 3)(3x + 4) = 6x² + 8x + 9x + 12 = 6x² + 17x + 12

Multiply coefficients and variables separately: 2x · 3x = 6x².

Example 4 - FOIL With a Zero Middle Term

(x + 5)(x − 5) = x² − 5x + 5x − 25 = x² − 25

The middle terms cancel. This is a difference of squares: (a + b)(a − b) = a² − b².

Example 5 - FOIL With Negative Coefficients

(2x − 3)(x − 4) = 2x² − 8x − 3x + 12 = 2x² − 11x + 12

The Last product is positive because (−3)(−4) = 12.