# 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.

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

Solution:

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.

Solution:

To find the area of a rectangle.

Given,

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