Answer :
To solve the problem of finding the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], let's break it down step-by-step:
1. Multiply the Coefficients:
We have three coefficients: 4, -3, and -7.
First, multiply these numbers together:
[tex]\[
4 \times (-3) = -12
\][/tex]
Then, multiply the result by -7:
[tex]\[
-12 \times (-7) = 84
\][/tex]
So, the product of the coefficients is 84.
2. Add the Exponents of [tex]\( x \)[/tex]:
Each term has an exponent for [tex]\( x \)[/tex]:
- The first term [tex]\( 4x \)[/tex] has [tex]\( x^1 \)[/tex].
- The second term [tex]\(-3x^8\)[/tex] has [tex]\( x^8 \)[/tex].
- The third term [tex]\(-7x^3\)[/tex] has [tex]\( x^3 \)[/tex].
Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So, the exponent for [tex]\( x \)[/tex] in the final product is 12.
3. Combine the Results:
Combine the result of the coefficients and the sum of the exponents:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
The correct answer is [tex]\(84x^{12}\)[/tex].
1. Multiply the Coefficients:
We have three coefficients: 4, -3, and -7.
First, multiply these numbers together:
[tex]\[
4 \times (-3) = -12
\][/tex]
Then, multiply the result by -7:
[tex]\[
-12 \times (-7) = 84
\][/tex]
So, the product of the coefficients is 84.
2. Add the Exponents of [tex]\( x \)[/tex]:
Each term has an exponent for [tex]\( x \)[/tex]:
- The first term [tex]\( 4x \)[/tex] has [tex]\( x^1 \)[/tex].
- The second term [tex]\(-3x^8\)[/tex] has [tex]\( x^8 \)[/tex].
- The third term [tex]\(-7x^3\)[/tex] has [tex]\( x^3 \)[/tex].
Add these exponents together:
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So, the exponent for [tex]\( x \)[/tex] in the final product is 12.
3. Combine the Results:
Combine the result of the coefficients and the sum of the exponents:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
The correct answer is [tex]\(84x^{12}\)[/tex].
