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

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

Answer :

To simplify the expression [tex]\(-4 x^2 (3 x - 7)\)[/tex], let's go through it step by step through the process of distribution:

1. Distribute the [tex]\(-4 x^2\)[/tex] across the terms inside the parentheses:

[tex]\[
-4 x^2 \cdot (3 x - 7)
\][/tex]

2. Apply the distributive property:

[tex]\[
-4 x^2 \cdot 3 x + (-4 x^2) \cdot (-7)
\][/tex]

3. Multiply each term separately:

- For the first term:
[tex]\[
-4 x^2 \cdot 3 x = -12 x^3
\][/tex]

- For the second term:
[tex]\[
-4 x^2 \cdot (-7) = 28 x^2
\][/tex]

4. Combine the simplified terms:

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

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

Now, we match this with the given options:

A. [tex]\(-12 x^3 + 28 x^2\)[/tex]

B. [tex]\(-12 x^3 - 28\)[/tex]

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

D. [tex]\(-12 x^3 + 28\)[/tex]

The correct answer is:

A. [tex]\(-12 x^3 + 28 x^2\)[/tex]