Question

Find the product of (2 - 5z)^2. Use algebra tiles if needed. Write the product in standard form.

Answer 1

To find the product of \((2 - 5z)^2\), we can use the formula for squaring a binomial, which is:

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

In our case, \(a = 2\) and \(b = 5z\). Now we can apply the formula:

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

2. Calculate \(2ab\):
\[
2ab = 2 \cdot 2 \cdot 5z = 20z
\]

3. Calculate \(b^2\):
\[
b^2 = (5z)^2 = 25z^2
\]

Now we can write the expression using the values we calculated:

\[
(2 - 5z)^2 = a^2 - 2ab + b^2 = 4 - 20z + 25z^2
\]

Next, we arrange the expression in standard form (descending powers of \(z\)):

\[
25z^2 - 20z + 4
\]

Thus, the product of \((2 - 5z)^2\) in standard form is:

\[
\boxed{25z^2 - 20z + 4}
\]