To evaluate the expression [tex]\((x+5) \cdot (x-5)^2\)[/tex] for [tex]\(x = 3\)[/tex], follow these steps:
1. Substitute [tex]\(x\)[/tex] with 3:
[tex]\[
(3 + 5) \cdot (3 - 5)^2
\][/tex]
2. Simplify inside the parentheses:
[tex]\[
3 + 5 = 8 \quad \text{and} \quad 3 - 5 = -2
\][/tex]
3. Square the result of [tex]\((3 - 5)\)[/tex]:
[tex]\[
(-2)^2 = 4
\][/tex]
4. Multiply the simplified results:
[tex]\[
8 \cdot 4
\][/tex]
5. Calculate the product:
[tex]\[
8 \cdot 4 = 32
\][/tex]
Thus, the value of the expression [tex]\((x+5) \cdot (x-5)^2\)[/tex] for [tex]\(x = 3\)[/tex] is:
[tex]\[
32
\][/tex]
From the given options, the correct answer is:
32
