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Select the correct answer.

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], you need to apply the distributive property. This property states that you multiply the term outside the parentheses by each term inside the parentheses. Let's break it down step-by-step:

1. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(3x\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times 3 = -12\)[/tex].
- Add the exponents of [tex]\(x\)[/tex]: [tex]\(x^2 \times x^1 = x^{2+1} = x^3\)[/tex].
- This gives us: [tex]\(-12x^3\)[/tex].

2. Distribute [tex]\(-4x^2\)[/tex] to [tex]\(-7\)[/tex]:
- Multiply the coefficients: [tex]\(-4 \times -7 = 28\)[/tex].
- The variable [tex]\(x\)[/tex] stays the same: [tex]\(x^2\)[/tex].
- This results in: [tex]\(28x^2\)[/tex].

3. Combine the terms:
- When you put both terms together, the expression simplifies to: [tex]\(-12x^3 + 28x^2\)[/tex].

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

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