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Answer :
To find the product [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], we can follow these steps:
1. Multiply the Coefficients:
- Start with the numbers (the coefficients) in front of the variables. You have [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiplying these together: [tex]\(4 \times (-3) \times (-7)\)[/tex].
- Calculate this step-by-step:
- [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]:
- The powers of [tex]\(x\)[/tex] are [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- When multiplying terms with the same base, add their exponents:
- [tex]\(1 + 8 + 3 = 12\)[/tex]
So, the power of [tex]\(x\)[/tex] in the product is [tex]\(x^{12}\)[/tex].
3. Combine the Results:
- Combine the product of the coefficients with the calculated power of [tex]\(x\)[/tex]:
- The final product is [tex]\(84x^{12}\)[/tex].
Therefore, the solution is [tex]\(84x^{12}\)[/tex], which corresponds to the option [tex]\(84 x^{12}\)[/tex].
1. Multiply the Coefficients:
- Start with the numbers (the coefficients) in front of the variables. You have [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiplying these together: [tex]\(4 \times (-3) \times (-7)\)[/tex].
- Calculate this step-by-step:
- [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]:
- The powers of [tex]\(x\)[/tex] are [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- When multiplying terms with the same base, add their exponents:
- [tex]\(1 + 8 + 3 = 12\)[/tex]
So, the power of [tex]\(x\)[/tex] in the product is [tex]\(x^{12}\)[/tex].
3. Combine the Results:
- Combine the product of the coefficients with the calculated power of [tex]\(x\)[/tex]:
- The final product is [tex]\(84x^{12}\)[/tex].
Therefore, the solution is [tex]\(84x^{12}\)[/tex], which corresponds to the option [tex]\(84 x^{12}\)[/tex].
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