Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], follow these steps:
1. Multiply the coefficients: Look at the numbers in front of the variables and multiply them together.
- Coefficients: [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply them: [tex]\(4 \times (-3) \times (-7)\)[/tex].
The result is:
[tex]\[
4 \times (-3) = -12
\][/tex]
[tex]\[
-12 \times (-7) = 84
\][/tex]
So, the product of the coefficients is [tex]\(84\)[/tex].
2. Add the exponents of [tex]\(x\)[/tex]: When multiplying terms with the same base (which is [tex]\(x\)[/tex] in this case), you add their exponents.
- For [tex]\(4x\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(1\)[/tex].
- For [tex]\(-3x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(8\)[/tex].
- For [tex]\(-7x^3\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(3\)[/tex].
Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results:
- The coefficient part is [tex]\(84\)[/tex].
- The exponent part is [tex]\(x^{12}\)[/tex].
Therefore, the product of the expression is [tex]\(84x^{12}\)[/tex].
This means that the correct answer to the question is [tex]\(84x^{12}\)[/tex].
1. Multiply the coefficients: Look at the numbers in front of the variables and multiply them together.
- Coefficients: [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply them: [tex]\(4 \times (-3) \times (-7)\)[/tex].
The result is:
[tex]\[
4 \times (-3) = -12
\][/tex]
[tex]\[
-12 \times (-7) = 84
\][/tex]
So, the product of the coefficients is [tex]\(84\)[/tex].
2. Add the exponents of [tex]\(x\)[/tex]: When multiplying terms with the same base (which is [tex]\(x\)[/tex] in this case), you add their exponents.
- For [tex]\(4x\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(1\)[/tex].
- For [tex]\(-3x^8\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(8\)[/tex].
- For [tex]\(-7x^3\)[/tex], the exponent of [tex]\(x\)[/tex] is [tex]\(3\)[/tex].
Add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results:
- The coefficient part is [tex]\(84\)[/tex].
- The exponent part is [tex]\(x^{12}\)[/tex].
Therefore, the product of the expression is [tex]\(84x^{12}\)[/tex].
This means that the correct answer to the question is [tex]\(84x^{12}\)[/tex].
