Let's expand the expression step by step. The given expression is:
[tex]\[ 2x^2(x + 3)(x - 2) \][/tex]
First, let's focus on expanding the expression [tex]\((x + 3)(x - 2)\)[/tex]:
[tex]\[
(x + 3)(x - 2)
\][/tex]
Using the distributive property (FOIL method), we get:
[tex]\[
x(x - 2) + 3(x - 2) = x^2 - 2x + 3x - 6 = x^2 + x - 6
\][/tex]
Now, we need to multiply this result by [tex]\(2x^2\)[/tex]:
[tex]\[
2x^2 (x^2 + x - 6)
\][/tex]
We will distribute [tex]\(2x^2\)[/tex] to each term inside the parentheses:
First term:
[tex]\[
2x^2 \cdot x^2 = 2x^4
\][/tex]
Second term:
[tex]\[
2x^2 \cdot x = 2x^3
\][/tex]
Third term:
[tex]\[
2x^2 \cdot (-6) = -12x^2
\][/tex]
So, combining all these terms together, the expanded form of the expression is:
[tex]\[
2x^4 + 2x^3 - 12x^2
\][/tex]
