College

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

Answer :

To simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex], we need to apply the distributive property. This property allows us to multiply each term inside the parentheses by the term outside the parentheses.

Here's the step-by-step process:

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

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

Explanation: Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex]. Then, multiply [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] to get [tex]\(x^{2+1} = x^3\)[/tex].

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

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

Explanation: Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex], and keep the [tex]\(x^2\)[/tex] as it is, since there is no [tex]\(x\)[/tex] term to combine from [tex]\(-7\)[/tex].

3. Combine the results: Bring the two terms together to form the simplified expression.

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

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

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

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