Answer :
Let's solve the problem step-by-step to find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex].
1. Multiply the Coefficients:
We start by multiplying the numerical coefficients in the expression. The coefficients here are 4, [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply these together:
[tex]\(4 \times (-3) = -12\)[/tex]
[tex]\(-12 \times (-7) = 84\)[/tex]
So, the total coefficient is [tex]\(84\)[/tex].
2. Add the Exponents of [tex]\(x\)[/tex]:
When multiplying terms with the same base, we add their exponents. The exponents of [tex]\(x\)[/tex] in this expression are 1 (from [tex]\(4x\)[/tex]), 8 (from [tex]\(-3x^8\)[/tex]), and 3 (from [tex]\(-7x^3\)[/tex]).
- Add these exponents together:
[tex]\(1 + 8 + 3 = 12\)[/tex]
This means the power of [tex]\(x\)[/tex] will be [tex]\(x^{12}\)[/tex].
3. Combine the Results:
Now that we have both the coefficient and the power of [tex]\(x\)[/tex], we combine them to form the final product of the expression:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
From the choices given, the correct answer is [tex]\(84x^{12}\)[/tex].
1. Multiply the Coefficients:
We start by multiplying the numerical coefficients in the expression. The coefficients here are 4, [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex].
- Multiply these together:
[tex]\(4 \times (-3) = -12\)[/tex]
[tex]\(-12 \times (-7) = 84\)[/tex]
So, the total coefficient is [tex]\(84\)[/tex].
2. Add the Exponents of [tex]\(x\)[/tex]:
When multiplying terms with the same base, we add their exponents. The exponents of [tex]\(x\)[/tex] in this expression are 1 (from [tex]\(4x\)[/tex]), 8 (from [tex]\(-3x^8\)[/tex]), and 3 (from [tex]\(-7x^3\)[/tex]).
- Add these exponents together:
[tex]\(1 + 8 + 3 = 12\)[/tex]
This means the power of [tex]\(x\)[/tex] will be [tex]\(x^{12}\)[/tex].
3. Combine the Results:
Now that we have both the coefficient and the power of [tex]\(x\)[/tex], we combine them to form the final product of the expression:
[tex]\[
84x^{12}
\][/tex]
Therefore, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
From the choices given, the correct answer is [tex]\(84x^{12}\)[/tex].
