Answer :
To solve the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] and find the product, follow these steps:
1. Multiply the Coefficients:
- First, look at the numbers in front of the variables. You have 4, [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply these together:
- [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]:
- Now, consider the exponents of [tex]\(x\)[/tex]. You have [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- Add these exponents together:
- [tex]\(1 + 8 + 3 = 12\)[/tex]
- So the sum of the exponents is [tex]\(12\)[/tex].
3. Combine the Results:
- Put together the product from the coefficients and the sum of the exponents. The expression becomes [tex]\(84x^{12}\)[/tex].
Therefore, the product of the given expression is [tex]\(\boxed{84x^{12}}\)[/tex].
1. Multiply the Coefficients:
- First, look at the numbers in front of the variables. You have 4, [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply these together:
- [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]:
- Now, consider the exponents of [tex]\(x\)[/tex]. You have [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- Add these exponents together:
- [tex]\(1 + 8 + 3 = 12\)[/tex]
- So the sum of the exponents is [tex]\(12\)[/tex].
3. Combine the Results:
- Put together the product from the coefficients and the sum of the exponents. The expression becomes [tex]\(84x^{12}\)[/tex].
Therefore, the product of the given expression is [tex]\(\boxed{84x^{12}}\)[/tex].
