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What is the product of the following expression?

[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 :

Sure, let's solve the problem step-by-step:

We have the expression: [tex]\((4x)(-3x^8)(-7x^3)\)[/tex].

Step 1: Multiply the coefficients.
- The coefficients we have are 4, -3, and -7.
- First, multiply 4 and -3:

[tex]\[
4 \times -3 = -12
\][/tex]

- Next, multiply the result by -7:

[tex]\[
-12 \times -7 = 84
\][/tex]

So, the product of the coefficients is 84.

Step 2: Multiply the variables.
- When multiplying variables with exponents, add the exponents together. The expression is [tex]\(x^1 \times x^8 \times x^3\)[/tex].
- Add the exponents:

[tex]\[
1 + 8 + 3 = 12
\][/tex]

This gives us [tex]\(x^{12}\)[/tex].

Step 3: Combine the results.
- Multiply the coefficient product (84) by the variable product ([tex]\(x^{12}\)[/tex]).

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

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

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