What is x^{n-1}*(x+y)-y(x^{n-1}+y^{n-1}) ?

The solution to x^{n-1}*(x+y)-y(x^{n-1}+y^{n-1}) is x^n-y^n

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simplify x^{n-1}*(x+y)-y(x^{n-1}+y^{n-1})

simplify

x^{n - 1} \cdot (x + y) - y (x^{n - 1} + y^{n - 1})

x^{n} - y^{n}

Solution steps

x^{n - 1} (x + y) - y (x^{n - 1} + y^{n - 1})

Expand

x^{n - 1} (x + y) : x^{n} + x^{n - 1} y

= x^{n} + x^{n - 1} y - y (x^{n - 1} + y^{n - 1})

Expand

- y (x^{n - 1} + y^{n - 1}) : - x^{n - 1} y - y^{n}

= x^{n} + x^{n - 1} y - x^{n - 1} y - y^{n}

Add similar elements:

x^{n - 1} y - x^{n - 1} y = 0

= x^{n} - y^{n}

(x^{3} + 1 + 3 x^{3} + 3 x)^{10}

(5 x \cdot y^{4})^{5} - (5 y^{4} \cdot x)^{3}

(3 x + 2)^{2} - (2 x - 3)^{2}

(x^{2} + 2 x - 3) (x^{2} + x - 2)

(a - b)^{3} + (a + b)^{3}

What is x^{n-1}*(x+y)-y(x^{n-1}+y^{n-1}) ?
The solution to x^{n-1}*(x+y)-y(x^{n-1}+y^{n-1}) is x^n-y^n