(2m+3)(2m-3)(m+4)

2 min read Jun 16, 2024

Factoring and Expanding (2m+3)(2m-3)(m+4)

This expression involves both factoring and expanding, so let's break it down step-by-step:

Recognizing the Difference of Squares

The first two terms, (2m+3) and (2m-3), represent a classic pattern: the difference of squares. This pattern occurs when you have two terms, one squared and the other squared, with a minus sign in between.

General form: (a + b)(a - b) = a² - b²
In our case: (2m + 3)(2m - 3) = (2m)² - (3)²

Expanding the Difference of Squares

Expanding the difference of squares:

(2m)² - (3)² = 4m² - 9

Multiplying the Remaining Factor

Now we have: (4m² - 9)(m + 4)

To multiply this out, we can use the distributive property (also known as FOIL):

First: 4m² * m = 4m³
Outer: 4m² * 4 = 16m²
Inner: -9 * m = -9m
Last: -9 * 4 = -36

Final Result

Combining the terms, we get the final expanded form:

(2m + 3)(2m - 3)(m + 4) = 4m³ + 16m² - 9m - 36