Sure! Let's simplify the expression [tex]\((y + 2)(y - 8)\)[/tex] step by step.
1. Apply the distributive property (also known as the FOIL method for multiplying binomials):
- First: Multiply the first terms in each binomial.
- Outer: Multiply the outer terms in each binomial.
- Inner: Multiply the inner terms in each binomial.
- Last: Multiply the last terms in each binomial.
So, we apply the distributive property:
[tex]\[
(y + 2)(y - 8)
\][/tex]
2. First, we multiply the first terms:
[tex]\[
y \cdot y = y^2
\][/tex]
3. Next, we multiply the outer terms:
[tex]\[
y \cdot (-8) = -8y
\][/tex]
4. Then, we multiply the inner terms:
[tex]\[
2 \cdot y = 2y
\][/tex]
5. Finally, we multiply the last terms:
[tex]\[
2 \cdot (-8) = -16
\][/tex]
6. Now, we combine all these results together:
[tex]\[
y^2 - 8y + 2y - 16
\][/tex]
7. Combine the like terms ([tex]\(-8y\)[/tex] and [tex]\(2y\)[/tex]):
[tex]\[
-8y + 2y = -6y
\][/tex]
8. Therefore, the simplified expression is:
[tex]\[
y^2 - 6y - 16
\][/tex]
So, the simplified form of [tex]\((y + 2)(y - 8)\)[/tex] is:
[tex]\[
y^2 - 6y - 16
\][/tex]
