FOIL Method Calculator

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FOIL Calculator

FOIL Method Calculator

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type or paste two expressions
like (x^2 - 3x)(x + 5) or (x - 5)^2

Answer:

12x² - 5x - 2

The FOIL Method Step-by-Step

Given:

(3x-2)(4x+1)

Multiply First, Outer, Inner, Last:

• First

3x • 4x

12x²

• Outer

3x • 1

• Inner

-2 • 4x

-8x

• Last

-2 • 1

-2

Put the terms together:

(12x²) + (3x) + (-8x) + (-2)

Combine like terms that share the same variables and exponents:

3x + -8x = -5x

Re-insert combined terms to get:

(12x²) + (-5x) + (-2)

Finally, remove parentheses and simplify signs. The expanded expression is:

12x² - 5x - 2

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Calculator Use

Multiply two binomial expressions using the FOIL method. See step-by-step instructions for multiplication with the FOIL method.

What is the FOIL Method?

In algebra, when an expression has two terms it is called a binomial. The FOIL method is a way to multiply two binomials or "expand the expression."

With FOIL you use the distributive property to multiply binomials like (a + b)(c + d). FOIL means multiply first terms, outer terms, inner terms and last terms.

After you multiply all terms, combine like terms and simplify the result.

What Does FOIL Stand For?

FOIL is short for First, Outer, Inner, Last and tells you how to multiply all terms in the expressions.

First: Multiply the first terms in each set of parentheses
Outer: Multiply the outer terms
Inner: Multiply the inner terms
Last: Multiply the last terms

Use the FOIL method to multiply binomials

What is the Distributive Property?

In algebra the distributive property says that
(a + b)(c + d) = ac + ad + bc + bd

So multiplying numbers that are added together equals multiplying the numbers and then adding them together.

The FOIL formula shows how the distributive property works. First, expand the expression by multiplying each term across the parentheses. Then simplify using addition or subtraction to get the final result.

Use the FOIL formula to multiply binomials

With the FOIL method you are using multiplication to "distribute" the a term to both c and d. Then you "distribute" the b term to c and d. Lastly, add everything together.

Be sure to respect the positive or negative signs of each product. This sum is the result of the binomial multiplication with the FOIL method.

Example Using the FOIL Method

Multiply the Binomials: (3x + 2)(4x + 1)

Multiply first terms: 3x • 4x = 12x²
Multiply outer terms: 3x • 1 = 3x
Multiply inner terms: 2 • 4x = 8x
Multiply last terms: 2 • 1 = 2

Then add these products together:

12x² + 3x + 8x + 2

Combine like terms 3x + 8x to get the final result:

12x² + 11x + 2

Using the FOIL method to multiply the binomials (3x + 2)(4x + 1) results in 12x² + 11x + 2.

FOIL and the Quadratic Equation

You may recognize equations that result from using the FOIL method as quadratic equations. These are "second order polynomials" which simply means the highest exponent on the variable in the equation is 2 as in "x squared."

In theory you could get a resulting expression that has an exponent greater than 2 after using the FOIL method. If your original expressions do not have exponents on the variables however, you will get a quadratic expression. Set it equal to zero and you have a quadratic equation like 12x² + 11x + 2 = 0.

The Quadratic Formula

You may need to find possible values for x, the variable in the binomials and your resulting polynomial. In this case you would use the quadratic formula:

\( x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a } \)

You can use this formula to solve quadratic equations where a ≠ 0. See the CalculatorSoup® Quadratic Formula Calculator for a deeper dive on this topic.