College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Select the correct answer.

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

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

Answer :

Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex] step-by-step:

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

- First term: [tex]\(-4x^2 \times 3x\)[/tex]

Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex]. Then, multiply the exponents of [tex]\(x\)[/tex] (i.e., [tex]\(x^2 \times x\)[/tex], which equals [tex]\(x^{2+1} = x^3\)[/tex]).

So, [tex]\(-4x^2 \times 3x = -12x^3\)[/tex].

- Second term: [tex]\(-4x^2 \times -7\)[/tex]

Here, multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex]. Since there's no [tex]\(x\)[/tex] in [tex]\(-7\)[/tex], multiply with the remaining [tex]\(x^2\)[/tex].

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

2. Combine the results:

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

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

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