(5a-4b)^2How to solve this problem

Question

asked Mar 8, 2024 110k views

2 Answers

Olivie · Answer 1 · 2024-03-14T22:45:36+0000

Hello!

Answer:

$\Large \boxed{\sf 25a^2-40ab + 16b^2}$

Explanation:

→ We want to simplify this expression:

$\sf (5a-4b)^2$

→ This expression is a remarkable identity:

We know that
$\sf (a-b)^2$ is equal to
$\sf a^2-2ab + b^2$ .

In our expression:

$\sf a = 5a\\b = 4b$

→ Let's apply this formula:

$\sf (5a)^2-2(5a)(4b) + (4b)^2$

→ Simplify the expression:

$\boxed{\sf 25a^2-40ab + 16b^2}$

Conclusion:

The expression (5a-4b)² is equal to 25a² - 40ab + 16b².