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Just as [tex]x^a-1 = (x-1)\sum_{n=0}^{a-1} x^n[/tex], is there a similar expansion for x^n - y^n?
The standard form of x^n - y^n is (x - y)(x^(n-1) + x^(n-2)y + x^(n-3)y^2 + ... + xy^(n-2) + y^(n-1)).
To expand x^n - y^n, you can use the formula (x - y)(x^(n-1) + x^(n-2)y + x^(n-3)y^2 + ... + xy^(n-2) + y^(n-1)).
The standard form is the simplified expression of x^n - y^n, while the expansion shows all the terms that are multiplied together to get to the standard form.
For example, the standard form of x^3 - y^3 is (x - y)(x^2 + xy + y^2). The expansion would be x^3 - x^2y - xy^2 + y^3.
The standard form and expansion of x^n - y^n can help in simplifying and solving equations, as well as identifying patterns and relationships between terms.