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What is the product?

[tex]\[(4x)(-3x^8)(-7x^3)\][/tex]

A. [tex]-84x^{12}[/tex]

B. [tex]-84x^{24}[/tex]

C. [tex]84x^{12}[/tex]

D. [tex]84x^{24}[/tex]

Answer :

To solve the problem of finding the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], let's break it down step-by-step:

1. Multiply the Coefficients:

We have three coefficients: 4, -3, and -7.
First, multiply these numbers together:
[tex]\[
4 \times (-3) = -12
\][/tex]
Then, multiply the result by -7:
[tex]\[
-12 \times (-7) = 84
\][/tex]

So, the product of the coefficients is 84.

2. Add the Exponents of [tex]\( x \)[/tex]:

Each term has an exponent for [tex]\( x \)[/tex]:
- The first term [tex]\( 4x \)[/tex] has [tex]\( x^1 \)[/tex].
- The second term [tex]\(-3x^8\)[/tex] has [tex]\( x^8 \)[/tex].
- The third term [tex]\(-7x^3\)[/tex] has [tex]\( x^3 \)[/tex].

Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]

So, the exponent for [tex]\( x \)[/tex] in the final product is 12.

3. Combine the Results:

Combine the result of the coefficients and the sum of the exponents:
[tex]\[
84x^{12}
\][/tex]

Therefore, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].

The correct answer is [tex]\(84x^{12}\)[/tex].

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