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

Answer :

To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we can use the distributive property, which means multiplying each term inside the parentheses by the term outside.

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

1. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(3x\)[/tex]:

[tex]\[
-4x^2 \times 3x = -12x^{3}
\][/tex]

Here we multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex], which gives [tex]\(-12\)[/tex], and then add the exponents of [tex]\(x\)[/tex], which results in [tex]\(x^{2+1} = x^{3}\)[/tex].

2. Multiply [tex]\(-4x^2\)[/tex] by [tex]\(-7\)[/tex]:

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

Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex], which gives [tex]\(28\)[/tex], and the [tex]\(x^2\)[/tex] remains unchanged.

Putting it all together, the simplified expression is:

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

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