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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^3-28[/tex]

C. [tex]-12x^3-28x^2[/tex]

D. [tex]-12x^3+28x^2[/tex]

Answer :

Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex].

Here's how you can do it step by step:

1. Distribute [tex]\(-4x^2\)[/tex] to both terms in the parentheses:
- First, multiply [tex]\(-4x^2\)[/tex] with [tex]\(3x\)[/tex]:
[tex]\[
-4x^2 \times 3x = -12x^3
\][/tex]

- Next, multiply [tex]\(-4x^2\)[/tex] with [tex]\(-7\)[/tex]:
[tex]\[
-4x^2 \times -7 = 28x^2
\][/tex]
(Remember: multiplying two negative numbers gives a positive result.)

2. Combine the results from the distribution:

The expression becomes:
[tex]\[
-12x^3 + 28x^2
\][/tex]

So, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].

From the given options, this corresponds to option D: [tex]\(-12x^3 + 28x^2\)[/tex].

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