Final Answer:
The terms in the expression are: -4y^3, -7x, 9y, 4.
The constants are: 4, -1.
The coefficients are: -4 (coefficient of y^3), -7 (coefficient of x), 9 (coefficient of y).
Step-by-step explanation:
Identifying terms, constants, and coefficients is essential in algebraic expressions. Terms are the individual components separated by addition or subtraction. In this expression, the terms are -4y^3, -7x, 9y, 4.
Constants are terms without variables. In this case, 4 and -1 are constants as they don't involve variables.
Coefficients are the numerical factors of the variables. For -4y^3, the coefficient is -4; for -7x, the coefficient is -7, and for 9y, the coefficient is 9.
Understanding these distinctions helps break down the expression into its basic components, facilitating further algebraic manipulations. It also provides insight into the impact each term has on the overall expression.
In summary, the terms encompass the entire expression, constants are terms without variables (4, -1), and coefficients are the numerical factors of the variables (-4, -7, 9). This breakdown aids in simplifying and analyzing algebraic expressions.