High School

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

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

Answer :

To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we will use the distributive property. This means we distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses.

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

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

3. Combine the two terms:
[tex]\[
-12x^3 + 28x^2
\][/tex]

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

The correct answer is B. [tex]\(-12x^3 + 28x^2\)[/tex].

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