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Answer :
To find the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], follow these steps:
1. Multiply the coefficients:
- The coefficients from each term are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- To find the product of these coefficients, multiply them together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- Notice the final result is positive because multiplying two negative numbers results in a positive number.
2. Add the exponents of [tex]\(x\)[/tex]:
- For the terms involving [tex]\(x\)[/tex], we have [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- To find the total power of [tex]\(x\)[/tex], add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results:
- The product of the expression is the product of the coefficients multiplied by [tex]\(x\)[/tex] raised to the total power obtained:
[tex]\[
84x^{12}
\][/tex]
So, the correct product is [tex]\(84x^{12}\)[/tex].
Therefore, the answer is: [tex]\(84x^{12}\)[/tex], which corresponds to the choice "84 x^{12}" in the original list of options.
1. Multiply the coefficients:
- The coefficients from each term are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- To find the product of these coefficients, multiply them together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- Notice the final result is positive because multiplying two negative numbers results in a positive number.
2. Add the exponents of [tex]\(x\)[/tex]:
- For the terms involving [tex]\(x\)[/tex], we have [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- To find the total power of [tex]\(x\)[/tex], add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results:
- The product of the expression is the product of the coefficients multiplied by [tex]\(x\)[/tex] raised to the total power obtained:
[tex]\[
84x^{12}
\][/tex]
So, the correct product is [tex]\(84x^{12}\)[/tex].
Therefore, the answer is: [tex]\(84x^{12}\)[/tex], which corresponds to the choice "84 x^{12}" in the original list of options.
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