Problem

$3(x+y)^{2}+5(x+y)=$

Answer

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Answer

\(\boxed{3x^{2} + 6xy + 5x + 3y^{2} + 5y}\) is the simplified form of the given expression.

Steps

Step 1 ：Given the algebraic expression $3(x+y)^{2}+5(x+y)$

Step 2 ：We can simplify it by using the distributive property of multiplication over addition. This means we can multiply each term inside the parentheses by the term outside the parentheses.

Step 3 ：Applying the distributive property, we get $5x + 5y + 3(x^{2} + 2xy + y^{2})$

Step 4 ：Further simplifying, we get $5x + 5y + 3x^{2} + 6xy + 3y^{2}$

Step 5 ：Rearranging the terms, we get $3x^{2} + 6xy + 5x + 3y^{2} + 5y$

Step 6 ：\(\boxed{3x^{2} + 6xy + 5x + 3y^{2} + 5y}\) is the simplified form of the given expression.

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