The expression (4xy) represents a monomial where 4 is the coefficient and (xy) is the product of the variables (x) and (y). It indicates that the value of the expression is obtained by multiplying 4 by the values of (x) and (y). This expression is often used in algebra to represent relationships in equations or to describe quantities in various mathematical contexts.
Without an equality sign the given expression is not an equation
The expression (4xy - 3xy + 2xy) consists of three terms: (4xy), (-3xy), and (2xy). Each term is a product of the coefficient (a number) and the variable part, which in this case is (xy). The coefficients are 4, -3, and 2, respectively. To combine the like terms, you would simplify the expression to ( (4 - 3 + 2)xy = 3xy).
To simplify the expression (3x - 2y - 4xy + 4y - 1x + 7xy), first combine like terms. Group the (x) terms: (3x - 1x = 2x), the (y) terms: (-2y + 4y = 2y), and the (xy) terms: (-4xy + 7xy = 3xy). This results in the simplified expression: (2x + 2y + 3xy).
The expression (2x + 2y) does not equal (2xy) or (4xy). Instead, it represents the sum of two terms, (2x) and (2y). If you factor it, you could write it as (2(x + y)), but it does not simplify to a product of (xy).
To simplify the expression (5xy + 2x^2 - xy - 3y^2), we first combine like terms. The terms involving (xy) are (5xy - xy), which simplifies to (4xy). Therefore, the simplified expression is (2x^2 + 4xy - 3y^2).
The difference of cubes has a formula. (4x - y)(16x2 + 4xy + y2)
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4xy).
Without an equality sign the given expression is not an equation
The expression (4xy - 3xy + 2xy) consists of three terms: (4xy), (-3xy), and (2xy). Each term is a product of the coefficient (a number) and the variable part, which in this case is (xy). The coefficients are 4, -3, and 2, respectively. To combine the like terms, you would simplify the expression to ( (4 - 3 + 2)xy = 3xy).
To simplify the expression (3x - 2y - 4xy + 4y - 1x + 7xy), first combine like terms. Group the (x) terms: (3x - 1x = 2x), the (y) terms: (-2y + 4y = 2y), and the (xy) terms: (-4xy + 7xy = 3xy). This results in the simplified expression: (2x + 2y + 3xy).
The expression (2x + 2y) does not equal (2xy) or (4xy). Instead, it represents the sum of two terms, (2x) and (2y). If you factor it, you could write it as (2(x + y)), but it does not simplify to a product of (xy).
To simplify the expression (5xy + 2x^2 - xy - 3y^2), we first combine like terms. The terms involving (xy) are (5xy - xy), which simplifies to (4xy). Therefore, the simplified expression is (2x^2 + 4xy - 3y^2).
3x2y - 4xy + 4x
4xy
To find the degree of the expression (2x - 4xy + 14xy + 3), we first simplify it to (2x + 10xy + 3). The degree of a term is determined by the sum of the exponents of the variables in that term. The term with the highest degree here is (10xy), which has a degree of 2 (1 from (x) and 1 from (y)). Therefore, the degree of the entire expression is 2.
The expressions (4xy - 9xy) and (12xy) are called terms because they each represent a single mathematical entity within an algebraic expression. Terms can consist of constants, variables, or the product of constants and variables. In this case, (4xy), (-9xy), and (12xy) are all terms that involve the variable (xy) multiplied by coefficients. When combined, they can be simplified and manipulated in algebraic operations.
It stays the same because it does not have any common terms. A: 6y-4xy