Foil Formula: Definition, Solved Examples

FOIL Formula can be referred to as a standard formula that is needed to multiply two binomials. This method is mostly used in elementary algebra. This FOIL is a mnemonic, which will help us in remembering the method of multiplying the two binomials. The “FOIL Formula” is an important formula that is required in solving algebraic equations. 

Key Terms: FOIL Formula, Uses, Distributive Law, Polynomials, Binomial Theorem

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How to use the FOIL Formula?

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The term “FOIL” is considered as an acronym for the four terms which are used in four terms of product.

(a+b)(c+d)=ac (First)+ ad(Outer) + bc(Inner) +bd (Last)

• First (the term is used for the first of each binomial that will be multiplied together)
• Outer (Outer terms of the binomial will be multiplied with each other)
• Inner (Inner terms of the binomial will be multiplied with each other)
• Last (Last terms of the binomial will be multiplied with each other

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FOIL Formula General Form

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In order to multiply the binomial, one must know the general form of FOIL Formula. The general form is given below:

(a+b)(c+d) = a(c+d)+b(c+d)

= ac+ ad+ bc+ bd

Foil Formula 

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FOIL Formula Example

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In order to multiply the linear binomials, the FOIL method is used. For example

(x+3)(x+5) = (x.x) + (x.5) +(3.x) + (3.5)

= X² + 5x+ 3x + 15

= x² + 8x + 15

If there is subtraction involved in the binomial, the corresponding terms in the equation should be negated. Let's consider another example:

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

= 6x² – 8x – 9x + 12

=6x² - 17x + 12

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FOIL Formula: Distributive Law

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The FOIL formula has the involvement of the distributive law. Hence. The method is a two-way process. In this process, there is an involvement of three applications of the distributive property. The distributive law along with the FOIL formula is generally applied in the case of trinomials and higher.

(a+b)(c+d) = a(c+d)+b(c+d)

= ac+ad+bc+bd

Here, the (c+d) is placed with the addition with the first binomial, which is the first step of the method. The second step involves the distributive law to simplify the two terms.

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FOIL Formula: Polynomials

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If we have to apply the FOIL Formula for a pair of Polynomials. We can make a table using the FOIL method, which is given below:

If we take an example- (a+b+c)(w+x+y+z) as polynomials, the degree of the terms can be found by anti-diagonally adding them.

In order to multiply these polynomials, we can use a table:

By summing up the entries of the table, the product of the polynomials will look like-

(a+b+c)(w+x+y+z) = (aw+ax+ay+az)+ (bw+bx+by+bz)+ (cw+cx+cy+cz)

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Things To Remember

• FOIL formula is used to multiply a binomial with another binomial
• The general form of FOIL Formula is (a+b)(c+d) = ac+ad+bc+bd
• Distributive law is along with FOIL Formula for trinomials or higher polynomials
• FOIL is mnemonic, which makes the multiplication process easy.