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Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we need to distribute the term [tex]\(-4x^2\)[/tex] across each term inside the parentheses. Let's go through the process step-by-step:
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -4 \times 3 \times x^2 \times x = -12x^3
\][/tex]
Here, we multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then multiply the powers of [tex]\(x\)[/tex] by adding exponents (since [tex]\(x^2 \times x\)[/tex] equals [tex]\(x^{2+1}\)[/tex] which is [tex]\(x^3\)[/tex]).
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = -4 \times -7 \times x^2 = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and the [tex]\(x^2\)[/tex] remains the same since there is no [tex]\(x\)[/tex] within the parentheses to combine with the [tex]\(x^2\)[/tex].
3. Combine the results:
The expression becomes [tex]\(-12x^3 + 28x^2\)[/tex].
Hence, the simplified form of the expression [tex]\(-4x^2(3x - 7)\)[/tex] is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the correct answer is option A: [tex]\(-12x^3 + 28x^2\)[/tex].
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -4 \times 3 \times x^2 \times x = -12x^3
\][/tex]
Here, we multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then multiply the powers of [tex]\(x\)[/tex] by adding exponents (since [tex]\(x^2 \times x\)[/tex] equals [tex]\(x^{2+1}\)[/tex] which is [tex]\(x^3\)[/tex]).
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = -4 \times -7 \times x^2 = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and the [tex]\(x^2\)[/tex] remains the same since there is no [tex]\(x\)[/tex] within the parentheses to combine with the [tex]\(x^2\)[/tex].
3. Combine the results:
The expression becomes [tex]\(-12x^3 + 28x^2\)[/tex].
Hence, the simplified form of the expression [tex]\(-4x^2(3x - 7)\)[/tex] is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the correct answer is option A: [tex]\(-12x^3 + 28x^2\)[/tex].
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