Answer :
Let's simplify the expression [tex]\(-3 x^3\left(-2 x^2+4 x-3\right)\)[/tex].
We need to distribute [tex]\(-3 x^3\)[/tex] into each term inside the parentheses:
1. Multiply [tex]\(-3 x^3\)[/tex] by [tex]\(-2 x^2\)[/tex]:
[tex]\[
-3 x^3 \times -2 x^2 = 6 x^{3+2} = 6 x^5
\][/tex]
2. Multiply [tex]\(-3 x^3\)[/tex] by [tex]\(4 x\)[/tex]:
[tex]\[
-3 x^3 \times 4 x = -12 x^{3+1} = -12 x^4
\][/tex]
3. Multiply [tex]\(-3 x^3\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-3 x^3 \times -3 = 9 x^3
\][/tex]
Now, combine all these results to get the simplified expression:
[tex]\[
6 x^5 - 12 x^4 + 9 x^3
\][/tex]
So, the simplified expression is:
[tex]\[
6 x^5 - 12 x^4 + 9 x^3
\][/tex]
We need to distribute [tex]\(-3 x^3\)[/tex] into each term inside the parentheses:
1. Multiply [tex]\(-3 x^3\)[/tex] by [tex]\(-2 x^2\)[/tex]:
[tex]\[
-3 x^3 \times -2 x^2 = 6 x^{3+2} = 6 x^5
\][/tex]
2. Multiply [tex]\(-3 x^3\)[/tex] by [tex]\(4 x\)[/tex]:
[tex]\[
-3 x^3 \times 4 x = -12 x^{3+1} = -12 x^4
\][/tex]
3. Multiply [tex]\(-3 x^3\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-3 x^3 \times -3 = 9 x^3
\][/tex]
Now, combine all these results to get the simplified expression:
[tex]\[
6 x^5 - 12 x^4 + 9 x^3
\][/tex]
So, the simplified expression is:
[tex]\[
6 x^5 - 12 x^4 + 9 x^3
\][/tex]
