(2a+3b)(2a-5b)

less than a minute read Jun 16, 2024

Multiplying Binomials: (2a+3b)(2a-5b)

This article will demonstrate how to multiply the binomials (2a + 3b) and (2a - 5b).

Understanding the Process

Multiplying binomials involves distributing each term of the first binomial to every term in the second binomial. This is often referred to as the FOIL method:

First terms: Multiply the first terms of each binomial.
Outer terms: Multiply the outer terms of the binomials.
Inner terms: Multiply the inner terms of the binomials.
Last terms: Multiply the last terms of each binomial.

Applying FOIL to (2a + 3b)(2a - 5b)

First: (2a)(2a) = 4a²
Outer: (2a)(-5b) = -10ab
Inner: (3b)(2a) = 6ab
Last: (3b)(-5b) = -15b²

Combining Like Terms

Now, combine the like terms:

4a² - 10ab + 6ab - 15b² = 4a² - 4ab - 15b²

Final Answer

Therefore, the product of (2a + 3b) and (2a - 5b) is 4a² - 4ab - 15b².