College

Simplify the expression [tex]$3(x+2)(x^2 - x - 8)$[/tex].

A. [tex]$3x^3 + 3x^2 - 30x - 48$[/tex]
B. [tex]$3x^3 + x^2 - 10x - 16$[/tex]
C. [tex]$3x^3 - 30x^2 - 12x - 48$[/tex]
D. [tex]$3x^3 - 4x^2 - 30x - 48$[/tex]

Answer :

Sure, let's break down the problem step by step to simplify the expression [tex]\( 3(x+2)(x^2 - x - 8) \)[/tex].

1. First, let's distribute the [tex]\( 3 \)[/tex] into [tex]\((x+2)\)[/tex]:

[tex]\[
3(x+2) = 3x + 6
\][/tex]

2. Now, let's focus on the polynomial [tex]\((x^2 - x - 8)\)[/tex]:

We have to distribute each term of [tex]\((3x + 6)\)[/tex] to every term of [tex]\((x^2 - x - 8)\)[/tex].

3. Distribute [tex]\(3x\)[/tex]:

[tex]\[
3x \cdot x^2 = 3x^3
\][/tex]
[tex]\[
3x \cdot (-x) = -3x^2
\][/tex]
[tex]\[
3x \cdot (-8) = -24x
\][/tex]

4. Distribute [tex]\(6\)[/tex]:

[tex]\[
6 \cdot x^2 = 6x^2
\][/tex]
[tex]\[
6 \cdot (-x) = -6x
\][/tex]
[tex]\[
6 \cdot (-8) = -48
\][/tex]

5. Combine all these terms together:

[tex]\[
3x^3 - 3x^2 - 24x + 6x^2 - 6x - 48
\][/tex]

6. Group like terms:

[tex]\[
3x^3 + (-3x^2 + 6x^2) + (-24x - 6x) - 48
\][/tex]

7. Simplify the like terms:

[tex]\[
3x^3 + 3x^2 - 30x - 48
\][/tex]

So, the simplified expression is:

[tex]\[ 3x^3 + 3x^2 - 30x - 48 \][/tex]

Therefore, the correct choice from the given options is:

[tex]\[ 3x^3 + 3x^2 - 30x - 48 \][/tex]

Other Questions