High School

Select the correct answer.

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]\(-4x^2(3x-7)\)[/tex], we can distribute [tex]\(-4x^2\)[/tex] across the expression inside the parentheses.

Here's a step-by-step solution:

1. Distribute [tex]\(-4x^2\)[/tex]:

Multiply [tex]\(-4x^2\)[/tex] with each term inside the parentheses [tex]\((3x - 7)\)[/tex]:

- [tex]\(-4x^2 \times 3x = -12x^3\)[/tex]
- [tex]\(-4x^2 \times (-7) = +28x^2\)[/tex]

2. Combine the results:

By combining these results, the expression becomes:

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

Now, let’s match this with the given options:

- 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]

The correct simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex], which matches option A.

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