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Answer :
Sure, let's simplify the expression step-by-step:
Given expression:
[tex]\[ 3(x + 2)(x^2 - x - 8) \][/tex]
Let's break it down into smaller steps:
1. Expand the inner expression first:
[tex]\[
(x + 2)(x^2 - x - 8)
\][/tex]
2. Distribute each term in [tex]\((x + 2)\)[/tex] across [tex]\((x^2 - x - 8)\)[/tex]:
[tex]\[
(x + 2) \times (x^2 - x - 8)
\][/tex]
This will give us:
[tex]\[
x \times (x^2 - x - 8) + 2 \times (x^2 - x - 8)
\][/tex]
3. Simplify the products:
- For [tex]\(x \times (x^2 - x - 8)\)[/tex]:
[tex]\[
x(x^2 - x - 8) = x^3 - x^2 - 8x
\][/tex]
- For [tex]\(2 \times (x^2 - x - 8)\)[/tex]:
[tex]\[
2(x^2 - x - 8) = 2x^2 - 2x - 16
\][/tex]
4. Combine the results:
[tex]\[
x^3 - x^2 - 8x + 2x^2 - 2x - 16
\][/tex]
5. Combine like terms:
[tex]\[
x^3 + (2x^2 - x^2) + (-8x - 2x) - 16
\][/tex]
[tex]\[
x^3 + x^2 - 10x - 16
\][/tex]
6. Multiply by the coefficient outside the parentheses:
[tex]\[
3(x^3 + x^2 - 10x - 16)
\][/tex]
7. Distribute the 3:
[tex]\[
3x^3 + 3x^2 - 30x - 48
\][/tex]
So, the simplified expression is:
[tex]\[ 3x^3 + 3x^2 - 30x - 48 \][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{3x^3 + 3x^2 - 30x - 48}
\][/tex]
Given expression:
[tex]\[ 3(x + 2)(x^2 - x - 8) \][/tex]
Let's break it down into smaller steps:
1. Expand the inner expression first:
[tex]\[
(x + 2)(x^2 - x - 8)
\][/tex]
2. Distribute each term in [tex]\((x + 2)\)[/tex] across [tex]\((x^2 - x - 8)\)[/tex]:
[tex]\[
(x + 2) \times (x^2 - x - 8)
\][/tex]
This will give us:
[tex]\[
x \times (x^2 - x - 8) + 2 \times (x^2 - x - 8)
\][/tex]
3. Simplify the products:
- For [tex]\(x \times (x^2 - x - 8)\)[/tex]:
[tex]\[
x(x^2 - x - 8) = x^3 - x^2 - 8x
\][/tex]
- For [tex]\(2 \times (x^2 - x - 8)\)[/tex]:
[tex]\[
2(x^2 - x - 8) = 2x^2 - 2x - 16
\][/tex]
4. Combine the results:
[tex]\[
x^3 - x^2 - 8x + 2x^2 - 2x - 16
\][/tex]
5. Combine like terms:
[tex]\[
x^3 + (2x^2 - x^2) + (-8x - 2x) - 16
\][/tex]
[tex]\[
x^3 + x^2 - 10x - 16
\][/tex]
6. Multiply by the coefficient outside the parentheses:
[tex]\[
3(x^3 + x^2 - 10x - 16)
\][/tex]
7. Distribute the 3:
[tex]\[
3x^3 + 3x^2 - 30x - 48
\][/tex]
So, the simplified expression is:
[tex]\[ 3x^3 + 3x^2 - 30x - 48 \][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{3x^3 + 3x^2 - 30x - 48}
\][/tex]
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Rewritten by : Barada
