Question

Find the product of (-4x - 3)^2. Use algebra tiles if needed. Write the product in standard form.

Answer 1

To find the product of \((-4x - 3)^2\), we can use the formula for squaring a binomial, which is \((a + b)^2 = a^2 + 2ab + b^2\).

Let:
\[
a = -4x \quad \text{and} \quad b = -3
\]

Now, we apply the formula:

1. Calculate \(a^2\):
\[
(-4x)^2 = 16x^2
\]

2. Calculate \(2ab\):
\[
2 \cdot (-4x) \cdot (-3) = 2 \cdot 12x = 24x
\]

3. Calculate \(b^2\):
\[
(-3)^2 = 9
\]

Now, putting it all together, we have:
\[
(-4x - 3)^2 = a^2 + 2ab + b^2 = 16x^2 + 24x + 9
\]

Thus, the product of \((-4x - 3)^2\) in standard form is:
\[
\boxed{16x^2 + 24x + 9}
\]