Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we will multiply the coefficients and add the exponents of [tex]\(x\)[/tex].
1. Multiply the coefficients:
The coefficients in the expression are 4, -3, and -7. We multiply these together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
The result is 84, which is positive because we are multiplying an even number of negative numbers.
2. Add the exponents of [tex]\(x\)[/tex]:
The expression involves the powers of [tex]\(x\)[/tex] as follows:
- The first term [tex]\(4x\)[/tex] is [tex]\(x^1\)[/tex].
- The second term [tex]\(-3x^8\)[/tex] is [tex]\(x^8\)[/tex].
- The third term [tex]\(-7x^3\)[/tex] is [tex]\(x^3\)[/tex].
When multiplying terms with the same base, we add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results:
With the coefficient of 84 and the power of [tex]\(x\)[/tex] being 12, the expression simplifies to:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
So, the correct choice is [tex]\(84 x^{12}\)[/tex].
1. Multiply the coefficients:
The coefficients in the expression are 4, -3, and -7. We multiply these together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
The result is 84, which is positive because we are multiplying an even number of negative numbers.
2. Add the exponents of [tex]\(x\)[/tex]:
The expression involves the powers of [tex]\(x\)[/tex] as follows:
- The first term [tex]\(4x\)[/tex] is [tex]\(x^1\)[/tex].
- The second term [tex]\(-3x^8\)[/tex] is [tex]\(x^8\)[/tex].
- The third term [tex]\(-7x^3\)[/tex] is [tex]\(x^3\)[/tex].
When multiplying terms with the same base, we add the exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Combine the results:
With the coefficient of 84 and the power of [tex]\(x\)[/tex] being 12, the expression simplifies to:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
So, the correct choice is [tex]\(84 x^{12}\)[/tex].
