Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we'll follow a series of steps:
1. Multiply the coefficients: Start by multiplying the numbers in front of the variables (the coefficients). We have:
- [tex]\(4\)[/tex]
- [tex]\(-3\)[/tex]
- [tex]\(-7\)[/tex]
Multiply these together:
[tex]\[
4 \times (-3) \times (-7)
\][/tex]
First, calculate [tex]\(4 \times (-3) = -12\)[/tex]. Then multiply this result by [tex]\(-7\)[/tex]:
[tex]\[
-12 \times (-7) = 84
\][/tex]
So, the product of the coefficients is [tex]\(84\)[/tex].
2. Add the exponents: Now, let's handle the exponents of [tex]\(x\)[/tex]. In the expression, we have:
- [tex]\(x^1\)[/tex] from [tex]\(4x\)[/tex]
- [tex]\(x^8\)[/tex] from [tex]\(-3x^8\)[/tex]
- [tex]\(x^3\)[/tex] from [tex]\(-7x^3\)[/tex]
Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So, the exponent for [tex]\(x\)[/tex] in the final expression is [tex]\(12\)[/tex].
3. Combine the results: Now we combine the product of the coefficients and the exponents to get the final expression:
[tex]\[
84x^{12}
\][/tex]
Based on this calculation, the correct and final product of the given expression is [tex]\(84x^{12}\)[/tex]. Therefore, the correct answer is [tex]\(84x^{12}\)[/tex].
1. Multiply the coefficients: Start by multiplying the numbers in front of the variables (the coefficients). We have:
- [tex]\(4\)[/tex]
- [tex]\(-3\)[/tex]
- [tex]\(-7\)[/tex]
Multiply these together:
[tex]\[
4 \times (-3) \times (-7)
\][/tex]
First, calculate [tex]\(4 \times (-3) = -12\)[/tex]. Then multiply this result by [tex]\(-7\)[/tex]:
[tex]\[
-12 \times (-7) = 84
\][/tex]
So, the product of the coefficients is [tex]\(84\)[/tex].
2. Add the exponents: Now, let's handle the exponents of [tex]\(x\)[/tex]. In the expression, we have:
- [tex]\(x^1\)[/tex] from [tex]\(4x\)[/tex]
- [tex]\(x^8\)[/tex] from [tex]\(-3x^8\)[/tex]
- [tex]\(x^3\)[/tex] from [tex]\(-7x^3\)[/tex]
Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So, the exponent for [tex]\(x\)[/tex] in the final expression is [tex]\(12\)[/tex].
3. Combine the results: Now we combine the product of the coefficients and the exponents to get the final expression:
[tex]\[
84x^{12}
\][/tex]
Based on this calculation, the correct and final product of the given expression is [tex]\(84x^{12}\)[/tex]. Therefore, the correct answer is [tex]\(84x^{12}\)[/tex].
