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Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we need to follow these steps:
1. Multiply the coefficients: Look at the numbers (without the variables) first. We have:
- [tex]\(4\)[/tex]
- [tex]\(-3\)[/tex]
- [tex]\(-7\)[/tex]
Multiply these numbers together:
[tex]\[
4 \times (-3) \times (-7)
\][/tex]
Multiplying two negative numbers gives a positive product. Therefore:
[tex]\[
4 \times (-3) = -12 \quad \Rightarrow \quad (-12) \times (-7) = 84
\][/tex]
2. Add the exponents: Now, consider the exponents of [tex]\(x\)[/tex]. When you multiply powers with the same base, you add their exponents. So, we have:
- [tex]\(x\)[/tex] is the same as [tex]\(x^1\)[/tex]
- [tex]\(x^8\)[/tex]
- [tex]\(x^3\)[/tex]
Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results: Plug in the calculated coefficient and the combined exponent into the expression to get the final product:
[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].
1. Multiply the coefficients: Look at the numbers (without the variables) first. We have:
- [tex]\(4\)[/tex]
- [tex]\(-3\)[/tex]
- [tex]\(-7\)[/tex]
Multiply these numbers together:
[tex]\[
4 \times (-3) \times (-7)
\][/tex]
Multiplying two negative numbers gives a positive product. Therefore:
[tex]\[
4 \times (-3) = -12 \quad \Rightarrow \quad (-12) \times (-7) = 84
\][/tex]
2. Add the exponents: Now, consider the exponents of [tex]\(x\)[/tex]. When you multiply powers with the same base, you add their exponents. So, we have:
- [tex]\(x\)[/tex] is the same as [tex]\(x^1\)[/tex]
- [tex]\(x^8\)[/tex]
- [tex]\(x^3\)[/tex]
Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results: Plug in the calculated coefficient and the combined exponent into the expression to get the final product:
[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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