(xy-1)(x-1)(y+1)-xy

Jasonbradley

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Jun 17, 2024

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Factoring and Simplifying the Expression (xy-1)(x-1)(y+1)-xy

This article explores the process of factoring and simplifying the given expression: (xy-1)(x-1)(y+1)-xy.

Expanding the Expression

We can begin by expanding the expression using the distributive property:

1. Expand (xy-1)(x-1): (xy-1)(x-1) = xy(x-1) - 1(x-1) = x²y - xy - x + 1

2. Multiply the expanded result by (y+1): (x²y - xy - x + 1)(y+1) = x²y(y+1) - xy(y+1) - x(y+1) + 1(y+1) = x²y² + x²y - xy² - xy - xy - x + y + 1

3. Combine like terms and subtract xy: x²y² + x²y - xy² - xy - xy - x + y + 1 - xy = x²y² + x²y - xy² - 3xy - x + y + 1

Factoring the Expression

While the expression can be simplified to the form above, it's not fully factored. Let's attempt to factor it further:

1. Look for common factors: The expression doesn't have any common factors that can be factored out.

2. Try grouping terms: We can try grouping terms to see if we can factor by grouping. However, this method doesn't lead to a straightforward factorization.

3. Consider the original form: The original form of the expression (xy-1)(x-1)(y+1)-xy might be the most simplified and factored form.

Conclusion

The expression (xy-1)(x-1)(y+1)-xy can be expanded and simplified to x²y² + x²y - xy² - 3xy - x + y + 1. However, it doesn't seem to have a simpler factored form that can be easily obtained through standard factorization techniques. The original form of the expression might be considered the most concise and factored representation.