Add. Simplify your answer. (-3x² + 2xy + 5y²) + (6x² + 8xy - y²)

Question image

Understand the Problem

The question is asking to simplify the addition of two polynomial expressions. The user needs to combine like terms in the expression (-3x² + 2xy + 5y²) + (6x² + 8xy - y²).

Answer

$$ 3x^2 + 10xy + 4y^2 $$
Answer for screen readers

$$ 3x^2 + 10xy + 4y^2 $$

Steps to Solve

  1. Organize the polynomial expressions First, write down the two polynomial expressions clearly: $$ (-3x^2 + 2xy + 5y^2) + (6x^2 + 8xy - y^2) $$

  2. Combine like terms Identify and combine the like terms from both expressions. The like terms are:

  • For $x^2$: $-3x^2 + 6x^2$
  • For $xy$: $2xy + 8xy$
  • For $y^2$: $5y^2 - y^2$
  1. Perform the additions for each group of like terms

    • For $x^2$: $$ -3x^2 + 6x^2 = 3x^2 $$

    • For $xy$: $$ 2xy + 8xy = 10xy $$

    • For $y^2$: $$ 5y^2 - y^2 = 4y^2 $$

  2. Write down the simplified polynomial Combine all the resulting terms: $$ 3x^2 + 10xy + 4y^2 $$

$$ 3x^2 + 10xy + 4y^2 $$

More Information

This expression is the simplified result of adding the two given polynomial expressions. Combining like terms is a fundamental concept in algebra that helps in simplifying mathematical expressions.

Tips

  • Forgetting to combine all like terms or missing some terms during addition.
  • Incorrectly adding the coefficients of the like terms (e.g., adding -3 and 6 incorrectly).

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser