Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we'll solve it step-by-step:
1. Calculate the Product of the Coefficients:
- The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply them 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]:
- We have [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- The exponents are [tex]\(1\)[/tex], [tex]\(8\)[/tex], and [tex]\(3\)[/tex], respectively.
- Add these exponents together:
[tex]\(1 + 8 + 3 = 12\)[/tex]
3. Combine the Result:
- The expression combines the coefficient and the variable [tex]\(x\)[/tex].
- Putting it all together, the product of the expression is [tex]\(84x^{12}\)[/tex].
Therefore, the correct option is [tex]\(\boxed{84x^{12}}\)[/tex].
1. Calculate the Product of the Coefficients:
- The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply them 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]:
- We have [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- The exponents are [tex]\(1\)[/tex], [tex]\(8\)[/tex], and [tex]\(3\)[/tex], respectively.
- Add these exponents together:
[tex]\(1 + 8 + 3 = 12\)[/tex]
3. Combine the Result:
- The expression combines the coefficient and the variable [tex]\(x\)[/tex].
- Putting it all together, the product of the expression is [tex]\(84x^{12}\)[/tex].
Therefore, the correct option is [tex]\(\boxed{84x^{12}}\)[/tex].
