Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we can follow these steps:
1. Multiply the coefficients (numbers):
- First, multiply [tex]\(4\)[/tex] and [tex]\(-3\)[/tex] to get [tex]\(-12\)[/tex].
- Next, multiply the result [tex]\(-12\)[/tex] by [tex]\(-7\)[/tex] to get [tex]\(84\)[/tex].
- So, the product of the coefficients is [tex]\(84\)[/tex].
2. Multiply the powers of [tex]\(x\)[/tex]:
- When multiplying terms with the same base, add the exponents. Here we have:
- [tex]\(x\)[/tex], which can be written as [tex]\(x^1\)[/tex].
- [tex]\(x^8\)[/tex], and
- [tex]\(x^3\)[/tex].
- Add the exponents: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the results:
- The final product of the expression is the coefficient multiplied by the base raised to the new exponent. So, we have:
[tex]\[
84x^{12}
\][/tex]
Thus, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
1. Multiply the coefficients (numbers):
- First, multiply [tex]\(4\)[/tex] and [tex]\(-3\)[/tex] to get [tex]\(-12\)[/tex].
- Next, multiply the result [tex]\(-12\)[/tex] by [tex]\(-7\)[/tex] to get [tex]\(84\)[/tex].
- So, the product of the coefficients is [tex]\(84\)[/tex].
2. Multiply the powers of [tex]\(x\)[/tex]:
- When multiplying terms with the same base, add the exponents. Here we have:
- [tex]\(x\)[/tex], which can be written as [tex]\(x^1\)[/tex].
- [tex]\(x^8\)[/tex], and
- [tex]\(x^3\)[/tex].
- Add the exponents: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the results:
- The final product of the expression is the coefficient multiplied by the base raised to the new exponent. So, we have:
[tex]\[
84x^{12}
\][/tex]
Thus, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
