(x^2+3xy+4y^2)-(2x^2-xy+3y^2-5)

Jasonbradley

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Jun 17, 2024

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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.