Foil Formula

FOIL Formula

The FOIL Formula is a typical formula that is required to multiply two binomials. This technique is commonly used in elementary algebra. This FOIL is a mnemonic that will help students remember how to multiply the two binomials. The FOIL Formula is a critical formula for solving algebraic problems. On the Extramarks website, students can access study materials on this topic.

The general form of the FOIL Formula is (a+b) (c+d) = ac + ad + bc + bd. Distributive Law FOIL Formula proceeds as follows. The distributive law is included in the FOIL Formula. Hence, the approach works in both directions. Three applications of the distributive property are involved in this procedure. In the case of trinomials and above, the distributive law, in conjunction with the FOIL Formula, is commonly used.

(a+b)(c+d) = a(c+d)+b(c+d) = ac+ad+bc+bd

The (c+d) is inserted with the addition of the first binomial, which is the method’s initial step. The distributive rule is used in the second step to simplify the two terms.

What Is FOIL Formula?

The FOIL Formula is a typical formula for multiplying two binomials. This FOIL Formula also aids in recalling the procedures involved in multiplying two binomials. When the bases are the same, students simply sum the powers of the base terms. FOIL is an acronym that stands for

  • F: First ( First term of each binomial is multiplied with each other)
  • O: Outer (Outer terms are multiplied with each other – e.g., a will be multiplied with d)
  • I: Inner (Inner terms are multiplied with each other – e.g., b will be multiplied with c)
  • L: Last (Last terms are multiplied with each other) ( Last terms of each binomial are multiplied with each other).

The general form of the FOIL Formula is (a+b) (c+d) = ac + ad + bc + bd. The FOIL Formula is used to multiply a binomial by another. This is the general FOIL Formula: (a+b)(c+d) = ac+ad+bc+bd. Along with FOIL, distributive law exists. FOIL is a mnemonic that facilitates multiplication.

Solved Examples Using FOIL Formula

  1. Multiply the binomial (2x + 3)(5x + 2) using the FOIL Formula


To find the product of (2x + 3) and (5x + 2).

using the FOIL Formula (a + b) (c + d) = ac + ad + bc + bd

(2x + 3)(5x + 2) = 2x×5x+2x×2+3×5x+3×22x×5x+2x×2+3×5x+3×2

= 10×2 + 4x + 15x + 6

= 10×2 + 19x + 6

The multiplication of (2x + 3)and (5x + 2) using the FOIL method is 10×2 + 19x + 6.

2. If a rectangle’s length is (2x+4) units and its width is (3x – 2) units. Using the FOIL Formula, determine its area.


To find the area of a rectangle.


Rectangle Length = (2x + 4) units

Rectangle Width = (3x + 2) units

Now, using the FOIL Formula (a + b) (c + d) = ac + ad + bc + bd

(2x + 4)(3x – 2) = 2x×3x+2x×(−2)+4×3x+4×(−2)2x×3x+2x×(−2)+4×3x+4×(−2)

= 6×2 – 4x + 12x – 8

= 6×2 + 8x – 8 square units

The area of a rectangle is 6×2 + 8x – 8 square units

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FAQs (Frequently Asked Questions)

1. What does FOIL stand for in Mathematics?

Many problems of Mathematics need to multiply two formulas together. When both expressions are binomials, the FOIL technique may be used to calculate the product. FOIL is a mathematical term that means to multiply two binomials together. FOIL stands for the order to multiply the binomial terms.

2. Why is the FOIL Formula effective?

FOIL is a method for remembering all of the processes involved in multiplying two binomials. The terms for each step that must be multiplied are as follows:

  • First, consider the first two terms of each binomial.
  • Outer -The first term in the first binomial and the last term in the second binomial are referred to as the outer terms.
  • Inner – the final term of the first binomial and the first term of the second binomial.
  • Last – the first binomial’s last phrase and the first binomial’s last term