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Answer :
To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we need to distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses. Here are the steps:
1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\(-4x^2 \times 3x = -12x^3\)[/tex]
This is done by multiplying the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then multiplying the variables [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] by adding their exponents ([tex]\(2 + 1 = 3\)[/tex]) to get [tex]\(x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\(-4x^2 \times -7 = 28x^2\)[/tex]
Here, multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and the [tex]\(x^2\)[/tex] stays as it is since there is no additional [tex]\(x\)[/tex] to multiply.
So, the expression [tex]\(-4x^2(3x - 7)\)[/tex] simplifies to:
[tex]\[ -12x^3 + 28x^2 \][/tex]
The correct answer is: D. [tex]\(-12x^3 + 28x^2\)[/tex]
1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\(-4x^2 \times 3x = -12x^3\)[/tex]
This is done by multiplying the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex], and then multiplying the variables [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] by adding their exponents ([tex]\(2 + 1 = 3\)[/tex]) to get [tex]\(x^3\)[/tex].
2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\(-4x^2 \times -7 = 28x^2\)[/tex]
Here, multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and the [tex]\(x^2\)[/tex] stays as it is since there is no additional [tex]\(x\)[/tex] to multiply.
So, the expression [tex]\(-4x^2(3x - 7)\)[/tex] simplifies to:
[tex]\[ -12x^3 + 28x^2 \][/tex]
The correct answer is: D. [tex]\(-12x^3 + 28x^2\)[/tex]
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