To find the simplified product of the expression [tex]\(-4 y^5(9 y + 6)\)[/tex], we can follow these steps:
1. Distribute the outer term across the inner terms:
[tex]\[
-4 y^5 (9 y + 6)
\][/tex]
This can be done by multiplying [tex]\(-4 y^5\)[/tex] with each term inside the parenthesis:
2. Multiply [tex]\(-4 y^5\)[/tex] by [tex]\(9 y\)[/tex]:
[tex]\[
-4 y^5 \cdot 9 y = -36 y^6
\][/tex]
Here’s why:
- [tex]\(-4\)[/tex] times [tex]\(9\)[/tex] equals [tex]\(-36\)[/tex].
- [tex]\(y^5\)[/tex] times [tex]\(y\)[/tex] equals [tex]\(y^{5+1} = y^6\)[/tex].
3. Multiply [tex]\(-4 y^5\)[/tex] by [tex]\(6\)[/tex]:
[tex]\[
-4 y^5 \cdot 6 = -24 y^5
\][/tex]
Here’s the breakdown:
- [tex]\(-4\)[/tex] times [tex]\(6\)[/tex] equals [tex]\(-24\)[/tex].
- The [tex]\(y^5\)[/tex] term remains [tex]\(y^5\)[/tex] because it’s only being multiplied by a constant [tex]\(6\)[/tex].
4. Combine the products:
[tex]\[
-36 y^6 + (-24 y^5)
\][/tex]
So, the simplified form of the expression [tex]\(-4 y^5(9 y + 6)\)[/tex] is:
[tex]\[
y^5(-36 y - 24)
\][/tex]
