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

Jasonbradley

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Jun 17, 2024

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Simplifying the Expression (x^2-2xy+2y^2)(x^2+y^2)+2x^3y-3x^2y^2+2xy^3

This article aims to simplify the given algebraic expression: (x^2-2xy+2y^2)(x^2+y^2)+2x^3y-3x^2y^2+2xy^3

1. Expanding the Parentheses:

We begin by expanding the product of the two binomials:

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

2. Combining Like Terms:

Now, let's combine the similar terms together:

x^4 + x^2y^2 - 2x^3y - 2xy^3 + 2x^2y^2 + 2y^4 + 2x^3y - 3x^2y^2 + 2xy^3

This simplifies to:

x^4 + 3x^2y^2 + 2y^4

3. Final Expression:

Therefore, the simplified form of the expression is x^4 + 3x^2y^2 + 2y^4.

Conclusion:

By carefully expanding the parentheses and combining like terms, we successfully simplified the complex expression. This method can be applied to simplify any similar algebraic expressions involving multiplication and addition.