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Answer :
Let's simplify the expression [tex]\(7x^2 (6x + 3x^2 - 4)\)[/tex] step-by-step.
1. Distribute [tex]\(7x^2\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[
7x^2 \times 6x = 42x^3
\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(3x^2\)[/tex]:
[tex]\[
7x^2 \times 3x^2 = 21x^4
\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
7x^2 \times (-4) = -28x^2
\][/tex]
2. Combine the results:
The simplified expression after distributing is:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
So, the correct simplification of [tex]\(7x^2 (6x + 3x^2 - 4)\)[/tex] is [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex].
The correct choice from the options provided is:
[tex]\[ \boxed{21x^4 + 42x^3 - 28x^2} \][/tex]
1. Distribute [tex]\(7x^2\)[/tex] to each term inside the parentheses:
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(6x\)[/tex]:
[tex]\[
7x^2 \times 6x = 42x^3
\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(3x^2\)[/tex]:
[tex]\[
7x^2 \times 3x^2 = 21x^4
\][/tex]
- Multiply [tex]\(7x^2\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[
7x^2 \times (-4) = -28x^2
\][/tex]
2. Combine the results:
The simplified expression after distributing is:
[tex]\[
21x^4 + 42x^3 - 28x^2
\][/tex]
So, the correct simplification of [tex]\(7x^2 (6x + 3x^2 - 4)\)[/tex] is [tex]\(21x^4 + 42x^3 - 28x^2\)[/tex].
The correct choice from the options provided is:
[tex]\[ \boxed{21x^4 + 42x^3 - 28x^2} \][/tex]
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