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Select the correct answer.

Simplify the expression [tex]$-4x^2(3x-7)$[/tex].

A. [tex]$-12x^3+28$[/tex]
B. [tex]$-12x^3-28x^2$[/tex]
C. [tex]$-12x^3-28$[/tex]
D. [tex]$-12x^3+28x^2$[/tex]

Answer :

Sure, let's simplify the expression step-by-step:

The given expression is [tex]\(-4x^2(3x - 7)\)[/tex].

To simplify this, we will use the distributive property, which states that [tex]\(a(b + c) = ab + ac\)[/tex].

1. Distributing [tex]\(-4x^2\)[/tex] to each term inside the parentheses:

- Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \cdot 3x = -12x^3
\][/tex]

- Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \cdot (-7) = 28x^2
\][/tex]

2. Combine the results from the distribution step:
[tex]\[
-12x^3 + 28x^2
\][/tex]

Therefore, the simplified expression is:
[tex]\[
-12x^3 + 28x^2
\][/tex]

So, the correct answer is:
D. [tex]\(-12x^3 + 28x^2\)[/tex]

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