Answer :
To find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex], you need to follow these steps:
1. Multiply the constants:
- First, extract the numerical coefficients from each term in the expression: [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply these numbers together: [tex]\(4 \times -3 \times -7\)[/tex].
- When multiplying, [tex]\(-3\)[/tex] and [tex]\(-7\)[/tex] give a positive result because the product of two negative numbers is positive. Then, multiply the positive result with [tex]\(4\)[/tex], which gives [tex]\(84\)[/tex].
2. Add the exponents of [tex]\(x\)[/tex]:
- Look at the powers of [tex]\(x\)[/tex] from each part of the expression: [tex]\(x^1\)[/tex] (from [tex]\(4x\)[/tex]), [tex]\(x^8\)[/tex] (from [tex]\(-3x^8\)[/tex]), and [tex]\(x^3\)[/tex] (from [tex]\(-7x^3\)[/tex]).
- Add the exponents: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the results:
- After calculating the product of the constants as [tex]\(84\)[/tex] and the sum of the exponents as [tex]\(12\)[/tex], the expression simplifies to [tex]\(84x^{12}\)[/tex].
Therefore, the final answer is [tex]\(84x^{12}\)[/tex]. The correct answer among the options provided is [tex]\(84 x^{12}\)[/tex].
1. Multiply the constants:
- First, extract the numerical coefficients from each term in the expression: [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply these numbers together: [tex]\(4 \times -3 \times -7\)[/tex].
- When multiplying, [tex]\(-3\)[/tex] and [tex]\(-7\)[/tex] give a positive result because the product of two negative numbers is positive. Then, multiply the positive result with [tex]\(4\)[/tex], which gives [tex]\(84\)[/tex].
2. Add the exponents of [tex]\(x\)[/tex]:
- Look at the powers of [tex]\(x\)[/tex] from each part of the expression: [tex]\(x^1\)[/tex] (from [tex]\(4x\)[/tex]), [tex]\(x^8\)[/tex] (from [tex]\(-3x^8\)[/tex]), and [tex]\(x^3\)[/tex] (from [tex]\(-7x^3\)[/tex]).
- Add the exponents: [tex]\(1 + 8 + 3 = 12\)[/tex].
3. Combine the results:
- After calculating the product of the constants as [tex]\(84\)[/tex] and the sum of the exponents as [tex]\(12\)[/tex], the expression simplifies to [tex]\(84x^{12}\)[/tex].
Therefore, the final answer is [tex]\(84x^{12}\)[/tex]. The correct answer among the options provided is [tex]\(84 x^{12}\)[/tex].
