FOIL Formula, Definition, Solved Examples

FOIL Formula: The FOIL formula, a standard method for multiplying two binomials, serves as a mnemonic to guide the steps involved in this multiplication process. It's a helpful composition representing the sequence of actions:

F stands for multiplying the First terms of each binomial.

O refers to the multiplication of the Outer terms.

I  represents the multiplication of the Inner terms.

L involves the multiplication of the Last terms of each binomial.

Remember, when the bases are identical, you simply add the powers of the base terms. Thus, the FOIL approach aids in the systematic multiplication of binomials.

What is the FOIL Formula

The basic structure of the FOIL formula can be expressed as:

When you multiply (a + b) by (c + d), the result follows the pattern:

FOIL Formula

(a + b)*(c + d)  = ac + ad + bc + bd.

FOIL Formula Solved Examples

Example 1: Multiply the binomial (4x - 2)(3x + 5) using the FOIL method.

Solution:

To find the product of (4x - 2) and (3x + 5):

Utilizing the FOIL Formula:

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

(4x - 2)(3x + 5) =

4x * 3x +

4x * 5 +

(-2) * 3x +

(-2) * 5 =

12x² + 20x - 6x - 10

= 12x² + 14x - 10

Answer: The multiplication of (4x - 2) and (3x + 5) using the FOIL method is 12x² + 14x - 10.

Example 2: If the side of a square is represented by (2x + 3), calculate its area using the FOIL method.

Solution:

To determine the area of the square:

Given:

Side of the square = (2x + 3)

Using the FOIL formula to find the area (A = side * side):

(2x + 3)(2x + 3) =

2x * 2x + 2x * 3 + 3 * 2x + 3 * 3 =

4x² + 6x + 6x + 9

= 4x² + 12x + 9 square units

Answer: The area of the square is 4x² + 12x + 9 square units.

This example demonstrates the application of the FOIL method in multiplication and area determination.

Example 3: Multiply the binomial (x + 2)(3x - 4) using the FOIL method.

Solution:

To find the product of (x + 2) and (3x - 4) using the FOIL method:

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

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

3x^2 - 4x + 6x - 8

= 3x^2 + 2x - 8

Answer: The multiplication of (x + 2) and (3x - 4) using the FOIL method is 3x^2 + 2x - 8.

Example 4: If the length of a rectangle is (4x + 5) units and its width is (2x - 3) units, determine its area using the FOIL method.

Solution:

To calculate the area of the rectangle:

Given:

Length of the rectangle = (4x + 5) units

Width of the rectangle = (2x - 3) units

Using the FOIL method to find the area (A = length * width):

(4x + 5)(2x - 3) =

4x * 2x + 4x * (-3) + 5 * 2x + 5 * (-3) =

8x^2 - 12x + 10x - 15

= 8x^2 - 2x - 15 square units

Answer: The area of the rectangle is 8x^2 - 2x - 15 square units.

This example illustrates further applications of the FOIL method in multiplying binomials and calculating the area of geometric shapes.

The FOIL method simplifies binomial multiplication by breaking down the process into steps—multiplying the First terms, Outer terms, Inner terms, and Last terms. It's particularly useful for algebraic expressions and geometry problems involving area calculations of squares and rectangles. Applying the FOIL approach allows for a systematic and structured solution in such scenarios.

The FOIL formula (a + b) * (c + d) = ac + ad + bc + bd serve as guiding principles in approaching binomial multiplication problems. It's a handy concept for students and individuals working in algebra, making complex multiplication more manageable and comprehensible.