Answer :
To simplify the expression [tex]\(3(x+2)(x^2-x-8)\)[/tex], let's go through the steps:
1. Start by distributing [tex]\( (x+2) \)[/tex] across each term in the polynomial [tex]\( (x^2-x-8) \)[/tex].
[tex]\((x+2) \times (x^2-x-8)\)[/tex] can be expanded as:
[tex]\((x+2) \cdot x^2\)[/tex] gives [tex]\( x^3 + 2x^2 \)[/tex].
[tex]\((x+2) \cdot (-x)\)[/tex] gives [tex]\(-x^2 - 2x\)[/tex].
[tex]\((x+2) \cdot (-8)\)[/tex] gives [tex]\(-8x - 16\)[/tex].
So, the expanded form is:
[tex]\[
x^3 + 2x^2 - x^2 - 2x - 8x - 16
\][/tex]
2. Combine like terms in the expanded polynomial:
[tex]\[
x^3 + (2x^2 - x^2) + (-2x - 8x) - 16
\][/tex]
This simplifies to:
[tex]\[
x^3 + x^2 - 10x - 16
\][/tex]
3. Now, multiply the simplified polynomial [tex]\( (x^3 + x^2 - 10x - 16) \)[/tex] by 3:
[tex]\[
3(x^3 + x^2 - 10x - 16)
\][/tex]
Multiply each term by 3:
[tex]\[
3 \cdot x^3 = 3x^3
\][/tex]
[tex]\[
3 \cdot x^2 = 3x^2
\][/tex]
[tex]\[
3 \cdot (-10x) = -30x
\][/tex]
[tex]\[
3 \cdot (-16) = -48
\][/tex]
4. Combine all the terms to write the final expression:
[tex]\[
3x^3 + 3x^2 - 30x - 48
\][/tex]
Therefore, the simplified expression is [tex]\( 3x^3 + 3x^2 - 30x - 48 \)[/tex].
1. Start by distributing [tex]\( (x+2) \)[/tex] across each term in the polynomial [tex]\( (x^2-x-8) \)[/tex].
[tex]\((x+2) \times (x^2-x-8)\)[/tex] can be expanded as:
[tex]\((x+2) \cdot x^2\)[/tex] gives [tex]\( x^3 + 2x^2 \)[/tex].
[tex]\((x+2) \cdot (-x)\)[/tex] gives [tex]\(-x^2 - 2x\)[/tex].
[tex]\((x+2) \cdot (-8)\)[/tex] gives [tex]\(-8x - 16\)[/tex].
So, the expanded form is:
[tex]\[
x^3 + 2x^2 - x^2 - 2x - 8x - 16
\][/tex]
2. Combine like terms in the expanded polynomial:
[tex]\[
x^3 + (2x^2 - x^2) + (-2x - 8x) - 16
\][/tex]
This simplifies to:
[tex]\[
x^3 + x^2 - 10x - 16
\][/tex]
3. Now, multiply the simplified polynomial [tex]\( (x^3 + x^2 - 10x - 16) \)[/tex] by 3:
[tex]\[
3(x^3 + x^2 - 10x - 16)
\][/tex]
Multiply each term by 3:
[tex]\[
3 \cdot x^3 = 3x^3
\][/tex]
[tex]\[
3 \cdot x^2 = 3x^2
\][/tex]
[tex]\[
3 \cdot (-10x) = -30x
\][/tex]
[tex]\[
3 \cdot (-16) = -48
\][/tex]
4. Combine all the terms to write the final expression:
[tex]\[
3x^3 + 3x^2 - 30x - 48
\][/tex]
Therefore, the simplified expression is [tex]\( 3x^3 + 3x^2 - 30x - 48 \)[/tex].
