To find the sum $$(3x^2 - 4xy + 5y^2) + (2x^2 - xy)$$, first rewrite the expression without parentheses to get $$3x^2 - 4xy + 5y^2 + 2x^2 - xy$$. Next, rearrange the terms to group the like terms together: $$3x^2 + 2x^2 - 4xy - xy + 5y^2$$. Finally, combine the like terms by adding their coefficients to get the simplified sum: $$5x^2 - 5xy + 5y^2$$.

Claude

To find the sum of the polynomials $$(u^2 - 6uv + 5v^2) + (3u^2 + 2uv)$$, follow these steps:  

First, distribute the addition, which simply removes the parentheses:  
$$u^2 - 6uv + 5v^2 + 3u^2 + 2uv$$

Next, rearrange the expression to group the like terms together:  
$$u^2 + 3u^2 - 6uv + 2uv + 5v^2$$

Finally, combine the like terms by adding their coefficients:  
$$4u^2 - 4uv + 5v^2$$

The sum is $$4u^2 - 4uv + 5v^2$$.

Finding the Sum $$(u^2 - 6uv + 5v^2) + (3u^2 + 2uv)$$

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OpenStax Intermediate Algebra

Finding the Sum $$(3x^2 - 4xy + 5y^2) + (2x^2 - xy)$$

To find the sum $$(2x^2 - 3xy - 2y^2) + (5x^2 - 3xy)$$, rewrite the expression without parentheses as $$2x^2 - 3xy - 2y^2 + 5x^2 - 3xy$$. Group the like terms together by rearranging the expression: $$2x^2 + 5x^2 - 3xy - 3xy - 2y^2$$. Combine the like terms by adding their coefficients to determine the final sum: $$7x^2 - 6xy - 2y^2$$.

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