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Expand the expression:

[tex]\[ 2x^2(x+3)(x-2) \][/tex]

A. [tex]\[ 2x^3 + 2x^2 - 12x \][/tex]

B. [tex]\[ 4x^3 + 6x^2 - 4x^2 \][/tex]

C. [tex]\[ 2x^4 + 2x^3 - 12x^2 \][/tex]

D. [tex]\[ 2x^3 + 2x^2 - 12x^2 \][/tex]

Sagot :

GinnyAnswer
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]
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