Answer :
To solve the problem of finding the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], follow these steps:
1. Multiply the Coefficients:
- The coefficients of the terms are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- First, multiply [tex]\(4\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[ 4 \times (-3) = -12 \][/tex]
- Next, multiply the result [tex]\(-12\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[ -12 \times (-7) = 84 \][/tex]
2. Add the Exponents:
- The exponents of [tex]\(x\)[/tex] in the terms 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 Results:
- Using the product of the coefficients and the sum of the exponents, the entire expression simplifies to:
[tex]\[ 84x^{12} \][/tex]
Therefore, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex]. So, the correct answer is [tex]\(84x^{12}\)[/tex].
1. Multiply the Coefficients:
- The coefficients of the terms are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- First, multiply [tex]\(4\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[ 4 \times (-3) = -12 \][/tex]
- Next, multiply the result [tex]\(-12\)[/tex] by [tex]\(-7\)[/tex]:
[tex]\[ -12 \times (-7) = 84 \][/tex]
2. Add the Exponents:
- The exponents of [tex]\(x\)[/tex] in the terms 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 Results:
- Using the product of the coefficients and the sum of the exponents, the entire expression simplifies to:
[tex]\[ 84x^{12} \][/tex]
Therefore, the product of [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex]. So, the correct answer is [tex]\(84x^{12}\)[/tex].
