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Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property, which means multiplying each term inside the parentheses by the term outside.
Here's how you do it step-by-step:
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{3}
\][/tex]
Here we multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex], which gives [tex]\(-12\)[/tex], and then add the exponents of [tex]\(x\)[/tex], which results in [tex]\(x^{2+1} = x^{3}\)[/tex].
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex], which gives [tex]\(28\)[/tex], and the [tex]\(x^2\)[/tex] remains unchanged.
Putting it all together, the simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
The correct answer is B: [tex]\(-12x^3 + 28x^2\)[/tex].
Here's how you do it step-by-step:
1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^{3}
\][/tex]
Here we multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex], which gives [tex]\(-12\)[/tex], and then add the exponents of [tex]\(x\)[/tex], which results in [tex]\(x^{2+1} = x^{3}\)[/tex].
2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times (-7) = 28x^2
\][/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex], which gives [tex]\(28\)[/tex], and the [tex]\(x^2\)[/tex] remains unchanged.
Putting it all together, the simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]
The correct answer is B: [tex]\(-12x^3 + 28x^2\)[/tex].
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