Question

final exam - requires respondus lockd
started: dec 10 at 6:50pm
quiz instructions
question 22
perform the indicated operation
(5a + 2b)(5a - 2b)
\\(\circ 25a^2 - 20ab + 4b^2\\)
\\(\circ 25a^2 + 4b^2\\)
\\(\circ 5a^2 - 2b^2\\)
\\(\circ 25a^2 - 4b^2\\)

Explanation:

Step1: Recall the difference of squares formula

The formula for the product of a sum and a difference is \((x + y)(x - y)=x^{2}-y^{2}\). Here, \(x = 5a\) and \(y=2b\).

Step2: Apply the formula

Substitute \(x = 5a\) and \(y = 2b\) into the formula \((x + y)(x - y)=x^{2}-y^{2}\). We get \((5a)^{2}-(2b)^{2}\).

Step3: Simplify the terms

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

Answer:

\(25a^{2}-4b^{2}\) (the last option, assuming the last option is \(25a^{2}-4b^{2}\))