Question

find the product. (simplify your answer completely.)
(4y + 1)^2

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a + b)^2\) is \(a^2 + 2ab + b^2\). Here, \(a = 4y\) and \(b = 1\).

Step2: Substitute \(a\) and \(b\) into the formula

First, calculate \(a^2\): \((4y)^2 = 16y^2\).
Then, calculate \(2ab\): \(2\times(4y)\times1 = 8y\).
Next, calculate \(b^2\): \(1^2 = 1\).

Step3: Combine the terms

Add the three terms together: \(16y^2 + 8y + 1\).

Answer:

\(16y^2 + 8y + 1\)