To multiply and simplify [tex]\((y-1)(y+8)\)[/tex], follow these steps:
1. Distribute each term in the first expression [tex]\( (y-1) \)[/tex] to each term in the second expression [tex]\( (y+8) \)[/tex].
2. First, distribute [tex]\( y \)[/tex] to both [tex]\( y \)[/tex] and [tex]\( 8 \)[/tex]:
[tex]\[
y \cdot y + y \cdot 8 = y^2 + 8y
\][/tex]
3. Next, distribute [tex]\( -1 \)[/tex] to both [tex]\( y \)[/tex] and [tex]\( 8 \)[/tex]:
[tex]\[
-1 \cdot y + (-1) \cdot 8 = -y - 8
\][/tex]
4. Combine all the distributed terms together:
[tex]\[
y^2 + 8y - y - 8
\][/tex]
5. Simplify the expression by combining like terms. In this case, combine the [tex]\( y \)[/tex] terms:
[tex]\[
y^2 + (8y - y) - 8 = y^2 + 7y - 8
\][/tex]
Therefore, the simplified expression is:
[tex]\[
y^2 + 7y - 8
\][/tex]
