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Expanding the Expression (x+y)(x^2-3xy+2y^2)
This article will guide you through the process of expanding the expression (x+y)(x^2-3xy+2y^2). This is a fundamental algebraic operation involving the distributive property.
Understanding the Expression
The given expression is a product of two factors:
- (x+y): A binomial containing two terms, 'x' and 'y'.
- (x^2-3xy+2y^2): A trinomial containing three terms, 'x^2', '-3xy', and '2y^2'.
Expanding the Expression
To expand this expression, we need to apply the distributive property. This means multiplying each term in the first factor (x+y) by each term in the second factor (x^2-3xy+2y^2).
Step 1: Multiply 'x' from the first factor by each term in the second factor.
- x * x^2 = x^3
- x * -3xy = -3x^2y
- x * 2y^2 = 2xy^2
Step 2: Multiply 'y' from the first factor by each term in the second factor.
- y * x^2 = x^2y
- y * -3xy = -3xy^2
- y * 2y^2 = 2y^3
Step 3: Combine all the terms obtained in steps 1 and 2.
(x+y)(x^2-3xy+2y^2) = x^3 - 3x^2y + 2xy^2 + x^2y - 3xy^2 + 2y^3
Step 4: Simplify the expression by combining like terms.
(x+y)(x^2-3xy+2y^2) = x^3 - 2x^2y - xy^2 + 2y^3
Conclusion
Therefore, the expanded form of the expression (x+y)(x^2-3xy+2y^2) is x^3 - 2x^2y - xy^2 + 2y^3. This process illustrates the power of the distributive property and how it can be used to simplify and manipulate algebraic expressions.