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Answer :
Let's simplify the given expression step-by-step:
[tex]\[ -4 x^2(3 x - 7) \][/tex]
Step 1:
First, let's distribute [tex]\(-4 x^2\)[/tex] to each term inside the parentheses.
Distribute [tex]\(-4 x^2\)[/tex] to [tex]\(3 x\)[/tex]:
[tex]\[ -4 x^2 \cdot 3 x = -12 x^3 \][/tex]
Step 2:
Next, distribute [tex]\(-4 x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[ -4 x^2 \cdot (-7) = 28 x^2 \][/tex]
Step 3:
Combine the results from Steps 1 and 2:
[tex]\[ -12 x^3 + 28 x^2 \][/tex]
Thus, the simplified expression is:
[tex]\[ -12 x^3 + 28 x^2 \][/tex]
Next, we need to find the correct answer from the given options. Comparing our simplified expression with the given options, we see that the correct answer is:
A. [tex]\( -12 x^3 - 28 x^2 \)[/tex] (This matches our simplified result exactly).
Therefore, the correct answer is A.
[tex]\[ -4 x^2(3 x - 7) \][/tex]
Step 1:
First, let's distribute [tex]\(-4 x^2\)[/tex] to each term inside the parentheses.
Distribute [tex]\(-4 x^2\)[/tex] to [tex]\(3 x\)[/tex]:
[tex]\[ -4 x^2 \cdot 3 x = -12 x^3 \][/tex]
Step 2:
Next, distribute [tex]\(-4 x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[ -4 x^2 \cdot (-7) = 28 x^2 \][/tex]
Step 3:
Combine the results from Steps 1 and 2:
[tex]\[ -12 x^3 + 28 x^2 \][/tex]
Thus, the simplified expression is:
[tex]\[ -12 x^3 + 28 x^2 \][/tex]
Next, we need to find the correct answer from the given options. Comparing our simplified expression with the given options, we see that the correct answer is:
A. [tex]\( -12 x^3 - 28 x^2 \)[/tex] (This matches our simplified result exactly).
Therefore, the correct answer is A.
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