Answer :
To solve the problem of finding the product of [tex]\((4x)\left(-3x^8\right)\left(-7x^3\right)\)[/tex], we need to multiply the coefficients and the variables separately. Here's how to do it step by step:
1. Multiply the coefficients:
- The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- First, multiply [tex]\(4 \times -3 = -12\)[/tex].
- Then, multiply [tex]\(-12 \times -7 = 84\)[/tex].
2. Multiply the variables:
- The variables are [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- When multiplying variables with the same base, you add the exponents. Here, [tex]\(x\)[/tex] is the same base:
[tex]\[
x^1 \times x^8 \times x^3 = x^{1+8+3} = x^{12}
\][/tex]
3. Combine the results:
- Combine the coefficient and the power of [tex]\(x\)[/tex] from the above steps.
- The resulting product is [tex]\(84x^{12}\)[/tex].
Therefore, the product of [tex]\((4x)\left(-3x^8\right)\left(-7x^3\right)\)[/tex] is [tex]\(84x^{12}\)[/tex]. The correct answer is [tex]\(84x^{12}\)[/tex].
1. Multiply the coefficients:
- The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- First, multiply [tex]\(4 \times -3 = -12\)[/tex].
- Then, multiply [tex]\(-12 \times -7 = 84\)[/tex].
2. Multiply the variables:
- The variables are [tex]\(x\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex].
- When multiplying variables with the same base, you add the exponents. Here, [tex]\(x\)[/tex] is the same base:
[tex]\[
x^1 \times x^8 \times x^3 = x^{1+8+3} = x^{12}
\][/tex]
3. Combine the results:
- Combine the coefficient and the power of [tex]\(x\)[/tex] from the above steps.
- The resulting product is [tex]\(84x^{12}\)[/tex].
Therefore, the product of [tex]\((4x)\left(-3x^8\right)\left(-7x^3\right)\)[/tex] is [tex]\(84x^{12}\)[/tex]. The correct answer is [tex]\(84x^{12}\)[/tex].
