Question

question 22
1 pts
perform the indicated operation.
(5a + 2b)(5a - 2b)
25a² - 20ab - 4b²
25a² + 4b²
5a² - 2b²
25a² - 4b²

Explanation:

Step1: Identify the formula

The expression \((5a + 2b)(5a - 2b)\) is a difference of squares, which follows the formula \((x + y)(x - y)=x^{2}-y^{2}\). Here, \(x = 5a\) and \(y=2b\).

Step2: Apply the formula

Substitute \(x = 5a\) and \(y = 2b\) into the formula:
\((5a)^{2}-(2b)^{2}\)

Step3: Simplify the terms

Calculate \((5a)^{2}=25a^{2}\) and \((2b)^{2} = 4b^{2}\). So the expression becomes \(25a^{2}-4b^{2}\).

Answer:

\(25a^{2}-4b^{2}\) (corresponding to the option with this expression)