Answer :
To solve the problem of finding the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], follow these steps:
1. Calculate the product of the coefficients:
- Multiply the numerical coefficients together: [tex]\(4 \times (-3) \times (-7)\)[/tex].
- When you multiply [tex]\(4 \times (-3)\)[/tex], you get [tex]\(-12\)[/tex].
- Then, multiply [tex]\(-12 \times (-7)\)[/tex] which gives you [tex]\(84\)[/tex].
2. Calculate the sum of the exponents for [tex]\(x\)[/tex]:
- In the expression [tex]\(4x\)[/tex], the exponent is [tex]\(1\)[/tex] (since [tex]\(x = x^1\)[/tex]).
- In the expression [tex]\(-3x^8\)[/tex], the exponent is [tex]\(8\)[/tex].
- In the expression [tex]\(-7x^3\)[/tex], the exponent is [tex]\(3\)[/tex].
- Add the exponents together: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the calculated values:
- The product of the coefficients results in [tex]\(84\)[/tex].
- The sum of the exponents for [tex]\(x\)[/tex] is [tex]\(12\)[/tex].
- Therefore, the product is [tex]\(84x^{12}\)[/tex].
So, the final answer is [tex]\(84x^{12}\)[/tex]. Therefore, the correct choice is [tex]\(84x^{12}\)[/tex].
1. Calculate the product of the coefficients:
- Multiply the numerical coefficients together: [tex]\(4 \times (-3) \times (-7)\)[/tex].
- When you multiply [tex]\(4 \times (-3)\)[/tex], you get [tex]\(-12\)[/tex].
- Then, multiply [tex]\(-12 \times (-7)\)[/tex] which gives you [tex]\(84\)[/tex].
2. Calculate the sum of the exponents for [tex]\(x\)[/tex]:
- In the expression [tex]\(4x\)[/tex], the exponent is [tex]\(1\)[/tex] (since [tex]\(x = x^1\)[/tex]).
- In the expression [tex]\(-3x^8\)[/tex], the exponent is [tex]\(8\)[/tex].
- In the expression [tex]\(-7x^3\)[/tex], the exponent is [tex]\(3\)[/tex].
- Add the exponents together: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the calculated values:
- The product of the coefficients results in [tex]\(84\)[/tex].
- The sum of the exponents for [tex]\(x\)[/tex] is [tex]\(12\)[/tex].
- Therefore, the product is [tex]\(84x^{12}\)[/tex].
So, the final answer is [tex]\(84x^{12}\)[/tex]. Therefore, the correct choice is [tex]\(84x^{12}\)[/tex].
