Answer :
Sure, let's break it down step-by-step!
We need to find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex].
1. Multiply the coefficients: The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex]. Let's multiply them together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
When you multiply [tex]\(-3\)[/tex] by [tex]\(-7\)[/tex], it becomes a positive number because the product of two negative numbers is positive. Then, multiplying by 4 gives 84.
2. Add the exponents of [tex]\(x\)[/tex]: In the expression, we have [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex]. To find the product of terms with the same base, you add the exponents (since they are being multiplied):
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So, the exponent for [tex]\(x\)[/tex] in the final expression will be [tex]\(x^{12}\)[/tex].
3. Combine both parts: Now, combine the coefficient and the result from the exponents:
[tex]\[
84x^{12}
\][/tex]
Thus, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
So, the correct answer is: [tex]\(84x^{12}\)[/tex].
We need to find the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex].
1. Multiply the coefficients: The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-7\)[/tex]. Let's multiply them together:
[tex]\[
4 \times (-3) \times (-7) = 84
\][/tex]
When you multiply [tex]\(-3\)[/tex] by [tex]\(-7\)[/tex], it becomes a positive number because the product of two negative numbers is positive. Then, multiplying by 4 gives 84.
2. Add the exponents of [tex]\(x\)[/tex]: In the expression, we have [tex]\(x^1\)[/tex], [tex]\(x^8\)[/tex], and [tex]\(x^3\)[/tex]. To find the product of terms with the same base, you add the exponents (since they are being multiplied):
[tex]\[
1 + 8 + 3 = 12
\][/tex]
So, the exponent for [tex]\(x\)[/tex] in the final expression will be [tex]\(x^{12}\)[/tex].
3. Combine both parts: Now, combine the coefficient and the result from the exponents:
[tex]\[
84x^{12}
\][/tex]
Thus, the product of the expression [tex]\((4x)(-3x^8)(-7x^3)\)[/tex] is [tex]\(84x^{12}\)[/tex].
So, the correct answer is: [tex]\(84x^{12}\)[/tex].
