Answer :
To find the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we can follow these steps:
1. Multiply the Coefficients:
- Start by multiplying the numerical coefficients of each term:
- The coefficient of the first term is [tex]\(4\)[/tex].
- The coefficient of the second term is [tex]\(-3\)[/tex].
- The coefficient of the third term is [tex]\(-7\)[/tex].
- Multiply these together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- When multiplying the negative numbers, remember that a negative times a negative results in a positive.
2. Combine the Powers of [tex]\(x\)[/tex]:
- Next, add the exponents of [tex]\(x\)[/tex] from each term:
- The exponent of [tex]\(x\)[/tex] in the first term is [tex]\(1\)[/tex] (since [tex]\(4x\)[/tex] can be written as [tex]\(4x^1\)[/tex]).
- The exponent of [tex]\(x\)[/tex] in the second term is [tex]\(8\)[/tex].
- The exponent of [tex]\(x\)[/tex] in the third term is [tex]\(3\)[/tex].
- Add these exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Form the Result:
- Combine the result of the coefficients and the exponents:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product is [tex]\(\boxed{84x^{12}}\)[/tex].
1. Multiply the Coefficients:
- Start by multiplying the numerical coefficients of each term:
- The coefficient of the first term is [tex]\(4\)[/tex].
- The coefficient of the second term is [tex]\(-3\)[/tex].
- The coefficient of the third term is [tex]\(-7\)[/tex].
- Multiply these together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
- When multiplying the negative numbers, remember that a negative times a negative results in a positive.
2. Combine the Powers of [tex]\(x\)[/tex]:
- Next, add the exponents of [tex]\(x\)[/tex] from each term:
- The exponent of [tex]\(x\)[/tex] in the first term is [tex]\(1\)[/tex] (since [tex]\(4x\)[/tex] can be written as [tex]\(4x^1\)[/tex]).
- The exponent of [tex]\(x\)[/tex] in the second term is [tex]\(8\)[/tex].
- The exponent of [tex]\(x\)[/tex] in the third term is [tex]\(3\)[/tex].
- Add these exponents:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
3. Form the Result:
- Combine the result of the coefficients and the exponents:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product is [tex]\(\boxed{84x^{12}}\)[/tex].
