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Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], let's follow these steps:
1. Multiply the Coefficients:
- We start by multiplying the coefficients of each term together.
- The coefficients are 4, -3, and -7.
- Multiply them: [tex]\(4 \times (-3) \times (-7)\)[/tex].
2. Calculate the Product of Coefficients:
- [tex]\(4 \times (-3) = -12\)[/tex].
- [tex]\(-12 \times (-7) = 84\)[/tex].
3. Combine the Powers of [tex]\(x\)[/tex]:
- For the variables [tex]\(x\)[/tex], add the exponents together because we are multiplying terms with the same base.
- The exponents are 1 (from [tex]\(4x\)[/tex]), 8 (from [tex]\(-3x^8\)[/tex]), and 3 (from [tex]\(-7x^3\)[/tex]).
- Add them: [tex]\(1 + 8 + 3 = 12\)[/tex].
4. Form the Final Product:
- Combine the product of the coefficients and the resultant power of [tex]\(x\)[/tex].
- The product is [tex]\(84x^{12}\)[/tex].
Therefore, the final result is [tex]\(84x^{12}\)[/tex].
1. Multiply the Coefficients:
- We start by multiplying the coefficients of each term together.
- The coefficients are 4, -3, and -7.
- Multiply them: [tex]\(4 \times (-3) \times (-7)\)[/tex].
2. Calculate the Product of Coefficients:
- [tex]\(4 \times (-3) = -12\)[/tex].
- [tex]\(-12 \times (-7) = 84\)[/tex].
3. Combine the Powers of [tex]\(x\)[/tex]:
- For the variables [tex]\(x\)[/tex], add the exponents together because we are multiplying terms with the same base.
- The exponents are 1 (from [tex]\(4x\)[/tex]), 8 (from [tex]\(-3x^8\)[/tex]), and 3 (from [tex]\(-7x^3\)[/tex]).
- Add them: [tex]\(1 + 8 + 3 = 12\)[/tex].
4. Form the Final Product:
- Combine the product of the coefficients and the resultant power of [tex]\(x\)[/tex].
- The product is [tex]\(84x^{12}\)[/tex].
Therefore, the final result is [tex]\(84x^{12}\)[/tex].
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