2 min read Jun 17, 2024

Simplifying Algebraic Expressions: (x^2+3xy+4y^2)-(2x^2-xy+3y^2-5)

This article will guide you through the process of simplifying the algebraic expression: (x^2+3xy+4y^2)-(2x^2-xy+3y^2-5).

Understanding the Expression

The expression consists of two parts:

  • (x^2+3xy+4y^2): This is a polynomial with three terms.
  • (2x^2-xy+3y^2-5): 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

  1. 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
  2. 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)
  3. 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^2-xy+3y^2-5) is -x^2 + 4xy + y^2 + 5.

Featured Posts