What is factor x^5y^5+3125 ?

The solution to factor x^5y^5+3125 is (xy+5)(x^4y^4-5x^3y^3+25x^2y^2-125xy+625)

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factor x^5y^5+3125

factor

x^{5} y^{5} + 3125

(x y + 5) (x^{4} y^{4} - 5 x^{3} y^{3} + 25 x^{2} y^{2} - 125 x y + 625)

Solution steps

x^{5} y^{5} + 3125

Rewrite

x^{5} y^{5}

(x y)^{5}

= (x y)^{5} + 3125

Apply radical rule:

a = (a)^{2}

Apply factoring rule:

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

n is odd

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

Refine

= (x y + 5) ((x y)^{4} - 5 (x y)^{3} + 25 (x y)^{2} - 125 x y + 625)

Simplify

(x y + 5) ((x y)^{4} - 5 (x y)^{3} + 25 (x y)^{2} - 125 x y + 625) : (x y + 5) (x^{4} y^{4} - 5 x^{3} y^{3} + 25 x^{2} y^{2} - 125 x y + 625)

= (x y + 5) (x^{4} y^{4} - 5 x^{3} y^{3} + 25 x^{2} y^{2} - 125 x y + 625)

a^{2} + 2 a (a + b) + (a + b)^{2}

10 + 221

(5 p^{2} - 3) + (2 p - 3 p^{3})

(x + Δ)^{(2)} - 4 (x + Δ)

17 d^{9} e^{4} - 51 e^{6}

What is factor x^5y^5+3125 ?
The solution to factor x^5y^5+3125 is (xy+5)(x^4y^4-5x^3y^3+25x^2y^2-125xy+625)