Question

– 4y3 + 4 – 7x + 9y - 1
List the terms.
List the constants.
List the coefficients.

Answer 1

The expression – 4y3 + 4 – 7x + 9y – 1 consists of terms, constants, and coefficients which have been listed respectively. No simplification of like terms is necessary in this case.

Step-by-step explanation:

The question is asking for the identification of various parts of the algebraic expression given as – 4y3 + 4 – 7x + 9y – 1. To answer this, we need to break down the expression into its individual components.

• Terms: The terms of an algebraic expression are the parts that are separated by the plus (+) or minus (–) signs. In this case, the terms are: – 4y3, +4, – 7x, +9y, – 1.
• Constants: Constants are the terms which do not contain any variables. The constants here are: +4, – 1.
• Coefficients: Coefficients are the numerical parts of the terms with variables. They include: – 4 (from – 4y3), – 7 (from – 7x), and +9 (from +9y).

Once the terms are listed, one should eliminate terms wherever possible to simplify the expression, though in this case, there are no like terms to combine.

Finally, always check the answer to ensure it is reasonable and meets the requirements of the question.

Answer 2

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.