What is factor a^5y^5-z^5 ?

The solution to factor a^5y^5-z^5 is (ay-z)(a^4y^4+a^3y^3z+a^2y^2z^2+ayz^3+z^4)

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factor a^5y^5-z^5

factor

a^{5} y^{5} - z^{5}

(a y - z) (a^{4} y^{4} + a^{3} y^{3} z + a^{2} y^{2} z^{2} + a y z^{3} + z^{4})

Solution steps

a^{5} y^{5} - z^{5}

Rewrite

a^{5} y^{5}

(a y)^{5}

= (a y)^{5} - z^{5}

Apply factoring rule:

x^{n} - y^{n} = (x - y) (x^{n - 1} + x^{n - 2} y + \dots + x y^{n - 2} y^{n - 1})

(a y)^{5} - z^{5} = (a y - z) ((a y)^{4} + (a y)^{3} z + (a y)^{2} z^{2} + a y z^{3} + z^{4})

= (a y - z) ((a y)^{4} + (a y)^{3} z + (a y)^{2} z^{2} + a y z^{3} + z^{4})

Simplify

(a y - z) ((a y)^{4} + (a y)^{3} z + (a y)^{2} z^{2} + a y z^{3} + z^{4}) : (a y - z) (a^{4} y^{4} + a^{3} y^{3} z + a^{2} y^{2} z^{2} + a y z^{3} + z^{4})

= (a y - z) (a^{4} y^{4} + a^{3} y^{3} z + a^{2} y^{2} z^{2} + a y z^{3} + z^{4})

(x - 4) + (5 x^{2})

(x^{2} - 10 x) + (y^{2} + 14 y)

x^{5} + x^{4} + (- x^{3})

7^{6} + 1000

- (0.04 x^{2})

What is factor a^5y^5-z^5 ?
The solution to factor a^5y^5-z^5 is (ay-z)(a^4y^4+a^3y^3z+a^2y^2z^2+ayz^3+z^4)