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Answer :
To simplify the expression [tex]\(-4x^2(3x-7)\)[/tex], we can use the distributive property. The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex].
Here's how the simplification works, step by step:
1. Distribute the [tex]\(-4x^2\)[/tex] across the terms inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^{2+1} = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
2. Combine the results from the distribution:
- The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Looking at the given options, the correct answer is:
D. [tex]\(-12x^3 + 28x^2\)[/tex]
Here's how the simplification works, step by step:
1. Distribute the [tex]\(-4x^2\)[/tex] across the terms inside the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^{2+1} = -12x^3
\][/tex]
- Next, multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]
2. Combine the results from the distribution:
- The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
Looking at the given options, the correct answer is:
D. [tex]\(-12x^3 + 28x^2\)[/tex]
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