Certainly! Let's go through the steps required to multiply and simplify the expression [tex]\((y - 4)(y + 3)\)[/tex].
### Step 1: Distribute Each Term
To expand the expression, we will use the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
1. First: Multiply the first terms in each binomial:
[tex]\[
y \cdot y = y^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
y \cdot 3 = 3y
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
-4 \cdot y = -4y
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-4 \cdot 3 = -12
\][/tex]
### Step 2: Combine Like Terms
Now, we combine all the products from the distributive step:
[tex]\[
y^2 + 3y - 4y - 12
\][/tex]
### Step 3: Simplify the Expression
Combine the like terms (those that have the same variable):
[tex]\[
y^2 + (3y - 4y) - 12
\][/tex]
Simplify the like terms:
[tex]\[
y^2 - y - 12
\][/tex]
### Final Simplified Expression
The simplified form of the expression [tex]\((y - 4)(y + 3)\)[/tex] is:
[tex]\[
y^2 - y - 12
\][/tex]
So, the result of multiplying and simplifying the expression [tex]\((y - 4)(y + 3)\)[/tex] is [tex]\(\boxed{y^2 - y - 12}\)[/tex].
