Simplifying Algebraic Expressions: (5x  xy^2)  (4xy^2  2x)
This article will guide you through the process of simplifying the algebraic expression: (5x  xy^2)  (4xy^2  2x).
Understanding the Expression
The expression involves variables (x and y) and coefficients (5, 1, 4, 2). We need to combine like terms to simplify it.
Steps to Simplify

Distribute the negative sign: The minus sign before the second set of parentheses means we multiply each term inside by 1.
(5x  xy^2) + (1)(4xy^2  2x)

Simplify: Multiply 1 with each term inside the parentheses.
5x  xy^2  4xy^2 + 2x

Combine like terms: Identify terms with the same variables and exponents.
(5x + 2x) + (xy^2  4xy^2)

Add coefficients: Combine the coefficients of like terms.
7x  5xy^2
Simplified Expression
The simplified form of the expression (5x  xy^2)  (4xy^2  2x) is 7x  5xy^2.