High School

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

Answer :

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

We need to simplify the expression:
[tex]\[ -4x^2(3x - 7) \][/tex]

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

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

- Next, multiply [tex]\( -4x^2 \)[/tex] by [tex]\( -7 \)[/tex]:
[tex]\[ -4x^2 \cdot -7 = 28x^2 \][/tex]

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

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

Therefore, the correct choice is:
B. [tex]\( -12x^3 + 28x^2 \)[/tex]