High School

Simplify: [tex]-3x^3(-2x^2 + 4x - 3)[/tex]

A. [tex]-6x^6 - 12x^4 + 9x^3[/tex]
B. [tex]6x^6 - 12x^3 + 9[/tex]
C. [tex]-5x^5 + x^4 - 6x^3[/tex]
D. [tex]6x^5 - 12x^4 + 9x^3[/tex]

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]