Answer :
To simplify the given expression [tex]\(-3x^3(-2x^2 + 4x - 3)\)[/tex], we will use the distributive property, which involves multiplying each term inside the parentheses by [tex]\(-3x^3\)[/tex].
Here is the step-by-step simplification process:
1. Distribute [tex]\(-3x^3\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(-3x^3\)[/tex] by [tex]\(-2x^2\)[/tex]:
[tex]\[
-3x^3 \times -2x^2 = 6x^{3+2} = 6x^5
\][/tex]
- Multiply [tex]\(-3x^3\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
-3x^3 \times 4x = -12x^{3+1} = -12x^4
\][/tex]
- Multiply [tex]\(-3x^3\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-3x^3 \times -3 = 9x^3
\][/tex]
2. Combine the results of the multiplication:
The simplified expression after distributing is:
[tex]\[
6x^5 - 12x^4 + 9x^3
\][/tex]
Therefore, the simplified form of the expression is [tex]\(6x^5 - 12x^4 + 9x^3\)[/tex].
Here is the step-by-step simplification process:
1. Distribute [tex]\(-3x^3\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(-3x^3\)[/tex] by [tex]\(-2x^2\)[/tex]:
[tex]\[
-3x^3 \times -2x^2 = 6x^{3+2} = 6x^5
\][/tex]
- Multiply [tex]\(-3x^3\)[/tex] by [tex]\(4x\)[/tex]:
[tex]\[
-3x^3 \times 4x = -12x^{3+1} = -12x^4
\][/tex]
- Multiply [tex]\(-3x^3\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-3x^3 \times -3 = 9x^3
\][/tex]
2. Combine the results of the multiplication:
The simplified expression after distributing is:
[tex]\[
6x^5 - 12x^4 + 9x^3
\][/tex]
Therefore, the simplified form of the expression is [tex]\(6x^5 - 12x^4 + 9x^3\)[/tex].
