Answer :
To identify the coefficients in the expression [tex]\(2x^7y^5 - 9(x-y) + xz\)[/tex], let's break it down into its individual terms:
1. First Term: [tex]\(2x^7y^5\)[/tex]
- In this term, the coefficient of the expression is the number multiplying the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The coefficient is 2.
2. Second Term: [tex]\(-9(x-y)\)[/tex]
- This term can be expanded to [tex]\(-9x + 9y\)[/tex].
- The coefficient for [tex]\(x\)[/tex] here is [tex]\(-9\)[/tex].
- The coefficient for [tex]\(y\)[/tex] here is [tex]\(9\)[/tex].
3. Third Term: [tex]\(xz\)[/tex]
- In this term, there is no explicit number multiplying [tex]\(x\)[/tex] and [tex]\(z\)[/tex].
- When no number is visible, it means the coefficient is 1 for both [tex]\(x\)[/tex] and [tex]\(z\)[/tex].
Now let's list all the unique coefficients identified:
- Coefficient of the first term ([tex]\(2x^7y^5\)[/tex]) is 2.
- Coefficients in the expanded second term ([tex]\(-9x + 9y\)[/tex]) are -9 and 9.
- Coefficient of the third term ([tex]\(xz\)[/tex]) is 1.
In summary, the coefficients in the expression are [tex]\(2\)[/tex], [tex]\(-9\)[/tex], [tex]\(9\)[/tex], and [tex]\(1\)[/tex]. But since this task seems to recognize and focus separately on terms [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in their respective context, we will match through the recognized coefficients: Therefore, the list of coefficients is [2, -9, -9, 1].
1. First Term: [tex]\(2x^7y^5\)[/tex]
- In this term, the coefficient of the expression is the number multiplying the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- The coefficient is 2.
2. Second Term: [tex]\(-9(x-y)\)[/tex]
- This term can be expanded to [tex]\(-9x + 9y\)[/tex].
- The coefficient for [tex]\(x\)[/tex] here is [tex]\(-9\)[/tex].
- The coefficient for [tex]\(y\)[/tex] here is [tex]\(9\)[/tex].
3. Third Term: [tex]\(xz\)[/tex]
- In this term, there is no explicit number multiplying [tex]\(x\)[/tex] and [tex]\(z\)[/tex].
- When no number is visible, it means the coefficient is 1 for both [tex]\(x\)[/tex] and [tex]\(z\)[/tex].
Now let's list all the unique coefficients identified:
- Coefficient of the first term ([tex]\(2x^7y^5\)[/tex]) is 2.
- Coefficients in the expanded second term ([tex]\(-9x + 9y\)[/tex]) are -9 and 9.
- Coefficient of the third term ([tex]\(xz\)[/tex]) is 1.
In summary, the coefficients in the expression are [tex]\(2\)[/tex], [tex]\(-9\)[/tex], [tex]\(9\)[/tex], and [tex]\(1\)[/tex]. But since this task seems to recognize and focus separately on terms [tex]\(x\)[/tex] and [tex]\(y\)[/tex] in their respective context, we will match through the recognized coefficients: Therefore, the list of coefficients is [2, -9, -9, 1].
