FOIL Formula

There is a standard formula for multiplying two binomials known as the FOIL formula. This FOIL formula also helps in remembering the steps required for multiplying two binomials. We must remember, when the bases are the same, we simply add the powers of the base terms. FOIL is actually a mnemonic.

FOIL stands for:
F: First ( First term of each binomial are 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 of each binomial are multiplied with each other).

What Is FOIL Formula?

The general form of FOIL formula is given below:

(a+b) (c+d) = ac + ad + bc + bd

Solved Examples Using FOIL Formula

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

Solution:

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

Now, using the FOIL Formula.

(a + b) (c + d) = ac + ad + bc + bd

(2x + 3)(5x + 2) = \(2x \times 5x + 2x \times 2 + 3 \times 5x + 3 \times 2\)

= 10x² + 4x + 15x + 6

= 10x² + 19x + 6

Answer: The multiplication of (2x + 3)and (5x + 2) using the FOIL method is 10x² + 19x + 6.

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

Solution:

To Find: The area of a rectangle.
Given,
Length of a rectangle = (2x + 4) units
Width of a rectangle = (3x + 2) units
Now, using the FOIL formula,
(a + b) (c + d) = ac + ad + bc + bd
(2x + 4)(3x - 2) = \(2x \times 3x + 2x \times (-2) + 4 \times 3x + 4 \times (-2)\)
= 6x² - 4x + 12x - 8
= 6x² + 8x - 8 square units

Answer: The area of a rectangle is 6x² + 8x - 8 square units.