To find the product [tex]\((r - 4)^2\)[/tex], we need to expand the expression. Let's do it step by step.
1. Understand the formula for squaring a binomial:
The general formula for squaring a binomial [tex]\((a - b)^2\)[/tex] is:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
2. Identify the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
In our expression [tex]\((r - 4)^2\)[/tex], we have [tex]\(a = r\)[/tex] and [tex]\(b = 4\)[/tex].
3. Apply the binomial square formula:
Substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula [tex]\((a - b)^2\)[/tex]:
[tex]\[
(r - 4)^2 = r^2 - 2 \cdot r \cdot 4 + 4^2
\][/tex]
4. Simplify each term:
- [tex]\(r^2\)[/tex] remains as [tex]\(r^2\)[/tex].
- [tex]\(-2 \cdot r \cdot 4\)[/tex] simplifies to [tex]\(-8r\)[/tex].
- [tex]\(4^2\)[/tex] calculates to [tex]\(16\)[/tex].
5. Combine all the terms:
Putting it all together, we get:
[tex]\[
(r - 4)^2 = r^2 - 8r + 16
\][/tex]
Therefore, the expanded expression for [tex]\((r - 4)^2\)[/tex] is:
[tex]\[
r^2 - 8*r + 16
\][/tex]
