Absolutely! Let's walk through the steps to simplify and solve the given problem in detail.
We begin by expanding and simplifying the product of two binomials:
[tex]\[
(y + 4)(y - 8)
\][/tex]
To expand this, we use the distributive property (also known as the FOIL method for binomials), where we multiply each term in the first binomial by each term in the second binomial. Here are the steps:
1. Multiply the first terms:
[tex]\[
y \times y = y^2
\][/tex]
2. Multiply the outer terms:
[tex]\[
y \times -8 = -8y
\][/tex]
3. Multiply the inner terms:
[tex]\[
4 \times y = 4y
\][/tex]
4. Multiply the last terms:
[tex]\[
4 \times -8 = -32
\][/tex]
Now, we combine all these results together:
[tex]\[
y^2 + (-8y) + 4y + (-32)
\][/tex]
Next, we simplify by combining like terms. The like terms here are [tex]\(-8y\)[/tex] and [tex]\(4y\)[/tex]:
[tex]\[
y^2 - 8y + 4y - 32
\][/tex]
[tex]\[
y^2 - 4y - 32
\][/tex]
So the expanded and simplified form of [tex]\((y + 4)(y - 8)\)[/tex] is:
[tex]\[
y^2 - 4y - 32
\][/tex]
Now let's consider the expression [tex]\(-6y - 12\)[/tex]. This expression is already in its simplest form as there are no like terms to combine. Therefore, it remains:
[tex]\[
-6y - 12
\][/tex]
To summarize:
1. The product of [tex]\((y + 4)(y - 8)\)[/tex] simplifies to:
[tex]\[
y^2 - 4y - 32
\][/tex]
2. The simplified expression [tex]\(-6y - 12\)[/tex] is:
[tex]\[
-6y - 12
\][/tex]
