(1-x-y)^2 Expand

Jasonbradley

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Jun 16, 2024

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Expanding (1-x-y)^2

The expression (1-x-y)^2 represents the square of a trinomial. Expanding this expression means multiplying the trinomial by itself. Here's how we can do it:

Understanding the Concept

The term (1-x-y)^2 is equivalent to (1-x-y) multiplied by itself:

(1-x-y)^2 = (1-x-y) * (1-x-y)

The Expansion Process

To expand the expression, we need to distribute each term of the first trinomial to each term of the second trinomial:

1. Multiply 1 from the first trinomial by each term in the second trinomial:

   • 1 * 1 = 1
   • 1 * (-x) = -x
   • 1 * (-y) = -y

2. Multiply -x from the first trinomial by each term in the second trinomial:

   • (-x) * 1 = -x
   • (-x) * (-x) = x^2
   • (-x) * (-y) = xy

3. Multiply -y from the first trinomial by each term in the second trinomial:

   • (-y) * 1 = -y
   • (-y) * (-x) = xy
   • (-y) * (-y) = y^2

Now, we have all the individual terms of the expansion. We need to combine the like terms:

1 - x - y - x + x^2 + xy - y + xy + y^2

Final Result

Combining the like terms, we get the expanded form of (1-x-y)^2:

(1-x-y)^2 = 1 - 2x - 2y + x^2 + 2xy + y^2

Therefore, the expanded form of (1-x-y)^2 is 1 - 2x - 2y + x^2 + 2xy + y^2.