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

2 min read Jun 16, 2024

Expanding the Expression (2a - 5b - 3)(2a - 5b + 2)

This article will guide you through the process of expanding the expression (2a - 5b - 3)(2a - 5b + 2) using the FOIL method and the distributive property.

Using the FOIL Method

The FOIL method stands for First, Outer, Inner, Last, and it's a helpful mnemonic for multiplying binomials. Let's break down the process:

First: Multiply the first terms of each binomial: (2a)(2a) = 4a²
Outer: Multiply the outer terms of each binomial: (2a)(2) = 4a
Inner: Multiply the inner terms of each binomial: (-5b)(2a) = -10ab
Last: Multiply the last terms of each binomial: (-5b)(2) = -10b

Now, we have the expanded form: 4a² + 4a - 10ab - 10b - 3(2a - 5b + 2)

Applying the Distributive Property

Next, we need to distribute the -3 to the terms inside the parentheses:

-3(2a - 5b + 2) = -6a + 15b - 6

Combining Like Terms

Finally, we combine the like terms:

4a² + 4a - 10ab - 10b - 6a + 15b - 6 = 4a² - 2a - 10ab + 5b - 6

Final Expanded Expression

Therefore, the expanded form of (2a - 5b - 3)(2a - 5b + 2) is 4a² - 2a - 10ab + 5b - 6.

Conclusion

Expanding expressions like this one is crucial in algebra and other areas of mathematics. By understanding the FOIL method and the distributive property, you can efficiently simplify and manipulate these expressions.