What is the coefficient of the term x^7y in the expansion of x(y^8)?

To find the coefficient of the term x⁷y in the expansion of x(y⁸), we can start by analyzing the expression involved in the expansion.

The expression x(y⁸) simplifies directly to xy⁸. Here, we identify that we’re dealing with a product of two variables: x and y. This expression does not expand further into any additional terms, as it’s simply composed of one multiply operation.

From this simplified form, it’s evident that there is only one term present: xy⁸. In this form, the x variable has an exponent of 1, and the y variable has an exponent of 8. Consequently, the coefficients for the various combinations of x and y can be directly observed. Specifically, the term x⁷y does not appear in this expression.

Therefore, the coefficient of x⁷y in the expansion of x(y⁸) is 0, since that term does not exist in this expansion.