Simplifying Algebraic Expressions: (x^2+3xy+4y^2)(2x^2xy+3y^25)
This article will guide you through the process of simplifying the algebraic expression: (x^2+3xy+4y^2)(2x^2xy+3y^25).
Understanding the Expression
The expression consists of two parts:
 (x^2+3xy+4y^2): This is a polynomial with three terms.
 (2x^2xy+3y^25): This is also a polynomial with four terms.
The minus sign between the parentheses indicates that we are subtracting the second polynomial from the first.
Simplifying the Expression

Distribute the negative sign:
 When subtracting a polynomial, we distribute the negative sign to each term within the second polynomial.
 This gives us: x^2 + 3xy + 4y^2  2x^2 + xy  3y^2 + 5

Combine like terms:
 Identify terms with the same variables and exponents.
 Combine their coefficients:
 x^2 terms: x^2  2x^2 = x^2
 xy terms: 3xy + xy = 4xy
 y^2 terms: 4y^2  3y^2 = y^2
 Constant terms: 5 (no other constant terms)

Write the simplified expression:
 Combine the simplified terms: x^2 + 4xy + y^2 + 5
Final Answer
The simplified form of the expression (x^2+3xy+4y^2)(2x^2xy+3y^25) is x^2 + 4xy + y^2 + 5.