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Choose the correct simplification of [tex]$7x^2(6x + 3x^2 - 4)$[/tex].

A. [tex]21x^4 - 42x^3 + 28x^2[/tex]
B. [tex]42x^4 + 21x^3 - 3x^2[/tex]
C. [tex]21x^4 + 42x^3 - 28x^2[/tex]
D. [tex]42x^4 - 13x^3 + 11x^2[/tex]

Answer :

Let's simplify the expression [tex]\(7 x^2(6 x + 3 x^2 - 4)\)[/tex] step-by-step.

1. Distribute [tex]\(7x^2\)[/tex] to every term inside the parentheses:

- Multiply [tex]\(7x^2\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[
7x^2 \cdot 6x = 42x^3
\][/tex]

- Multiply [tex]\(7x^2\)[/tex] by [tex]\(3x^2\)[/tex]:
[tex]\[
7x^2 \cdot 3x^2 = 21x^4
\][/tex]

- Multiply [tex]\(7x^2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
7x^2 \cdot (-4) = -28x^2
\][/tex]

2. Combine all the resulting terms:

[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]

This results in the simplified expression: [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex].

Therefore, the correct choice is [tex]\(\boxed{21x^4 + 42x^3 - 28x^2}\)[/tex].

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