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Find the product:

3(x + 4)(x - 5)

A. [tex]\( 3x^2 - 11x - 20 \)[/tex]
B. [tex]\( 3x^2 - 20x \)[/tex]
C. [tex]\( 3x^2 - 3x - 60 \)[/tex]
D. [tex]\( 3x^2 - x - 20 \)[/tex]

Sagot :

GinnyAnswer
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]
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