Foil Calculator is a free online tool that simplifies the given equation. Using STUDYQUERIES’s foil calculator tool makes the calculation faster, and it displays the simplification value in a fraction of a second.

How to Use the Foil Calculator?

To use the foil calculator, follow these steps:

  • Step 1: Put the expression into the input field
  • Step 2: Click “Calculate” to get the simplification
  • Step 3: The simplified expression will be displayed in the output field

Foil Calculator

What Is Foil Method And Calculator?

FOIL (first, outer, inner, and last) is an efficient way of remembering how to multiply two binomials in a very organized manner.

FOIL refers to the following acronym:

$$\color{red}{First}\Longrightarrow\pmb{\color{Blue}{F}}$$

$$\color{red}{Outer}\Longrightarrow\pmb{\color{Blue}{O}}$$

$$\color{red}{Inner}\Longrightarrow\pmb{\color{Blue}{I}}$$

$$\color{red}{Last}\Longrightarrow\pmb{\color{Blue}{L}}$$

The acronym FOIL stands for first, outer, inner, and last.

Foil Calculator
Foil Calculator

In order to put this into perspective, suppose we want to multiply two binomials, $$\left( {a + b} \right)\left( {c + d} \right)$$

The first means multiplying the terms that appear in the first position of each binomial.

$$\left( {\color{red}{a} + b} \right)\left( {\color{red}{c} + d} \right)=\color{red}{a.c}+\_$$

The outer means to multiply the terms that are located at the ends (outermost) of the two binomials when written side-by-side.

$$\left( {\color{red}{a} + b} \right)\left( {c + \color{red}{d}} \right)=a.c+\color{red}{a.d}+\_$$

The inner means to multiply the middle two terms of the binomials when they are side-by-side.

$$\left( {a + \color{red}{b}} \right)\left( {\color{red}{c} + d} \right)=a.c+b.d+\color{red}{b.c}+\_$$

The last means multiplying the terms in the last position of each binomial.

$$\left( {a + \color{red}{b}} \right)\left( {c + \color{red}{d}} \right)=a.c+b.d+b.c+\color{red}{b.d}$$

Taking the four (4) partial products from the first, outer, inner and last, we simply add them together to obtain the final answer.

How Can We Use The FOIL Method In Multiplication Of Binomial Expressions?

\(\pmb{\color{red}{Multiply\ the\ binomials \left( {x + 5} \right)\left( {x – 3} \right)\ using\ the\ FOIL\ Method.}}\)

Multiply the pair of terms from each binomial in the first position.

\(\left( {\color{red}{x} + 5} \right)\left( {\color{red}{x} – 3} \right)=\color{red}{x^2}\)

When the two binomials are written side by side, multiply the outer terms.

\(\left( {\color{red}{x} + 5} \right)\left( {x \color{red}{-3}} \right)=x^2-\color{red}{3x}\)

When you write the two binomials side by side, multiply their inner terms.

\(\left( {x + \color{red}{5}} \right)\left( {\color{red}{x} – 3} \right)=x^2-3x+\color{red}{5x}\)

Multiply the pair of terms in each binomial from the last position.

\(\left( {x + \color{red}{5}} \right)\left( {x \color{red}{-3}} \right)=x^2-3x+5x-\color{red}{15}\)

Lastly, combine like terms to simplify. The middle terms can be combined with the variable x.

\(x^2\color{red}{-3x}+\color{red}{5x}-15=x^2+\color{red}{2x}-15\)

\(\pmb{\color{red}{Multiply\ the\ binomials \left( {3x – 7} \right)\left( {2x + 1} \right)\ using\ the\ FOIL\ Method.}}\)

If the first presentation on how to multiply binomials using FOIL did not make sense to you. Let me show you another approach. In this way, you will be exposed to different approaches to addressing the same type of problem with a different approach.

Multiply the first two terms

\(\left( {\color{red}{3x} – 7} \right)\left( {\color{red}{2x} +1} \right)=\color{red}{6x^2}\)

By multiplying the outer terms

\(\left( {\color{red}{3x} – 7} \right)\left( {2x+ \color{red}{1}} \right)=6x^2+\color{red}{3x}\)

Multiply the inner terms

\(\left( {3x \color{red}{-7}} \right)\left( {\color{red}{2x} +1} \right)=6x^2+3x \color{red}{-14x}\)

Multiply the last terms

\(\left( {3x \color{red}{-7}} \right)\left( {2x+ \color{red}{1}} \right)=6x^2+3x-14x \color{red}{-7}\)

Using FOIL, we arrive at this polynomial, which can be simplified by combining similar terms. In order to get a single value, the two middle x-terms can be subtracted. Combine the terms 3x and -14x that are similar in the middle.

\(6x^2+\color{red}{3x}-\color{red}{14x}-7=6x^2\color{red}{-11x}-7\)

\(\pmb{\color{red}{Multiply\ the\ binomials \left( { -4x + 5} \right)\left( {x + 1} \right)\ using\ the\ FOIL\ Method.}}\)

Another way of doing this is to list the four partial products, and then add them together to get the answer.

Multiply the first terms: \((-4x)\times (x)=\color{red}{-4x^2}\)

Multiply the outer terms: \((-4x)\times(1)=\color{red}{-4x}\)

Multiply the inner terms: \((5)\times(x)=\color{red}{5x}\)

Multiply the last terms: \((5)\times(1)=\color{red}{5}\)

Get the sum of the partial products, and then combine similar terms.

\((-4x^2)+(-4x)+(5x)+(5) = -4x^2+x+5\)

\(\pmb{\color{red}{Multiply\ the\ binomials \left( { -7x – 3} \right)\left( { -2x + 8} \right)\ using\ the\ FOIL\ Method.}}\)

Multiply the first terms: \((-7x)\times (-2x)=\color{red}{14x^2}\)

Multiply the outer terms: \((-7x)\times(8)=\color{red}{-56x}\)

Multiply the inner terms: \((-3)\times(-2x)=\color{red}{+6x}\)

Multiply the last terms: \((-3)\times(8)=\color{red}{-24}\)

Finally, combine like terms to finish this off!

\(\left( { -7x – 3} \right)\left( { -2x + 8} \right)=(14x^2)+(-56x)+(6x)+(-24) = -14x^2-50x-24\)

\(\pmb{\color{red}{Multiply\ the\ binomials \left( { -x – 1} \right)\left( { -x + 1} \right).

Multiply the first terms: \((-x)\times (-x)=\color{red}{x^2}\)

Multiply the outer terms: \((-x)\times(1)=\color{red}{-x}\)

Multiply the inner terms: \((-1)\times(-x)=\color{red}{+x}\)

Multiply the last terms: \((-1)\times(1)=\color{red}{-1}\)

Finally, combine like terms to finish this off!

\(\left( { -7x – 3} \right)\left( { -2x + 8} \right)=(x^2)+(-x)+(x)+(-1) = x^2-1\)

\(\pmb{\color{red}{Multiply\ the\ binomials \left( {6x + 5} \right)\left( {5x + 3} \right).

Multiply the first terms: \((6x)\times (5x)=\color{red}{30x^2}\)

Multiply the outer terms: \((6x)\times(3)=\color{red}{18x}\)

Multiply the inner terms: \((5)\times(5x)=\color{red}{25x}\)

Multiply the last terms: \((5)\times(3)=\color{red}{15}\)

Finally, combine like terms to finish this off!

\(\left( { -7x – 3} \right)\left( { -2x + 8} \right)=(30x^2)+(18x)+(25x)+(15) = 30x^2+43x+15\)

FAQs

How do you FOIL in math?

  • First – multiply the first terms.
  • Outside – multiply the outside/outer terms.
  • Inside – multiply the inside/inner terms.
  • Last – multiply the last terms.

How do you FOIL numbers in front of parentheses?

That is, foil tells you to multiply the first terms in each of the parentheses, then multiply the two terms that are on the “outside” (furthest from each other), then the two terms that are on the “inside” (closest to each other), and then the last terms in each of the parentheses.

What does L stand for in the FOIL method?

The FOIL method is made up of four multiplication steps. Let’s see what each letter in FOIL stands for one a time. The ‘F’ stands for first. The ‘O’ stands for outside. The ‘I’ stands for inside, and the ‘L’ stands for last.

How do multiply fractions?

There are 3 simple steps to multiply fractions

  • Multiply the top numbers (the numerators).
  • Multiply the bottom numbers (the denominators).
  • Simplify the fraction if needed.

What is factored form in algebra?

A factored form is a parenthesized algebraic expression. In effect, a factored form is a product of sums of products … or a sum of products of sums. Any logic function can be represented by a factored form, and any factored form is a representation of some logic function.

How do you distribute 4 Binomials?

  • Break the first binomial into its two terms.
  • Distribute each term of the first binomial over the other terms.
  • Multiply the terms.
  • Simplify and combine any like terms.

Is FOIL distributive property?

Using FOIL to Multiply Binomials. A shortcut called FOIL is sometimes used to find the product of two binomials. The FOIL method arises out of the distributive property. We are simply multiplying each term of the first binomial by each term of the second binomial, and then combining like terms.

Who made FOIL math?

Hidden behind this simple acronym lies a step-by-step guide to solving a seemly difficult mathematical problem. Coined by William Betz in his 1929 textbook, Algebra for Today, the FOIL technique of multiplying two binomials is widely known by children and adults all around the world.

Is FOIL a mathematical concept?

In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials—hence the method may be referred to as the FOIL method.