To find the product of the given expression [tex]\( 3(x+4)(x-5) \)[/tex] and select the correct answer, let's go through the problem step-by-step:
1. First, identify the expression to expand:
[tex]\[
3(x + 4)(x - 5)
\][/tex]
2. Step 1: Expand the binomials [tex]\((x+4)\)[/tex] and [tex]\((x-5)\)[/tex]:
We apply the distributive property (also known as the FOIL method for binomials).
[tex]\( (x + 4)(x - 5) \)[/tex]
[tex]\[
x^2 - 5x + 4x - 20
\][/tex]
Combine like terms:
[tex]\[
x^2 - x - 20
\][/tex]
3. Step 2: Multiply the expanded binomial by 3:
Distribute the 3 across the terms [tex]\(x^2 - x - 20\)[/tex]:
[tex]\[
3 \cdot (x^2 - x - 20)
\][/tex]
Distribute each term:
[tex]\[
3x^2 - 3x - 60
\][/tex]
4. Final result:
The expanded expression is:
[tex]\[
3x^2 - 3x - 60
\][/tex]
So, the correct answer from the choices provided is:
C. [tex]\( 3 x^2 - 3 x - 60 \)[/tex]
