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FOIL Calculator

Enter the two binomial expressions you wish to expand using the FOIL method. Ensure they are in the format (ax + b)(cx + d), then click 'Calculate. '

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FOIL Calculator

Use our online FOIL Calculator to multiply any two binomials step by step. Learn how the FOIL method works and expand algebraic expressions quickly and accurately.

What Is the FOIL Method?

The FOIL method is an algebraic technique for multiplying two binomials, such as (x + y)(a + b). FOIL breaks the multiplication into four parts:

First: Multiply the first terms in each binomial
Outer: Multiply the outermost terms
Inner: Multiply the innermost terms
Last: Multiply the last terms in each binomial

Once these steps are completed, combine all like terms to simplify the expression. Essentially, FOIL is a systematic way to apply the distributive property.

FOIL Formula:

FOIL Formula

Distributive Property Explained

The distributive property states:

"Multiplying a sum by a term is the same as multiplying each addend separately and then adding the products."

Example: x(y + z) = xy + xz

FOIL applies this principle. For example, multiplying (w + x)(y + z):

(w + x)(y + z)

= w(y + z) + x(y + z) (distribute each term of the first binomial)

= wy + wz + xy + xz (expand each product)

FOIL Method Examples

Example #1

Multiply: (2x + 1)(5x + 7)

Solution:

First: 2x × 5x = 10x²
Outer: 2x × 7 = 14x
Inner: 1 × 5x = 5x
Last: 1 × 7 = 7

Combine terms: 10x² + 14x + 5x + 7 = 10x² + 19x + 7

Example #2

Multiply: (4x - 5)(x - 7)

Solution:

First: 4x × x = 4x²
Outer: 4x × -7 = -28x
Inner: -5 × x = -5x
Last: -5 × -7 = 35

Combine terms: 4x² - 28x - 5x + 35 = 4x² - 33x + 35

For accurate and faster results, try the online FOIL calculator.

Factoring and Reverse FOIL

Factoring is the reverse process of FOIL. While FOIL expands binomials into a polynomial, factoring splits a polynomial back into binomials:

FOIL Example: (x + 2)(x + 3) = x² + 5x + 6
Factoring Example: x² + 5x + 6 = (x + 2)(x + 3)

Use our factoring calculator for reversing FOIL.

Using the FOIL Calculator

Enter the two binomials in the format "(ax + b)(cx + d)"
Click "Calculate" to see the expanded result
Step-by-step FOIL calculations will be displayed

Perform multiple calculations by clicking "Re-Calculate."

FAQs

Is FOIL Only for Binomials?

Yes, FOIL applies specifically to binomials. For polynomials with more than two terms, use the distributive property. Try our Distributive Property Calculator.