What is factor (x^5y^5)-1 ?

The solution to factor (x^5y^5)-1 is (xy-1)(x^4y^4+x^3y^3+x^2y^2+xy+1)

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factor (x^5y^5)-1

factor

(x^{5} y^{5}) - 1

(x y - 1) (x^{4} y^{4} + x^{3} y^{3} + x^{2} y^{2} + x y + 1)

Solution steps

(x^{5} y^{5}) - 1

Remove parentheses:

(a) = a

= x^{5} y^{5} - 1

Rewrite

x^{5} y^{5}

(x y)^{5}

= (x y)^{5} - 1

Rewrite

1

1^{5}

= (x y)^{5} - 1^{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})

(x y)^{5} - 1^{5} = (x y - 1) ((x y)^{4} + (x y)^{3} + (x y)^{2} + x y + 1)

= (x y - 1) ((x y)^{4} + (x y)^{3} + (x y)^{2} + x y + 1)

Simplify

(x y - 1) ((x y)^{4} + (x y)^{3} + (x y)^{2} + x y + 1) : (x y - 1) (x^{4} y^{4} + x^{3} y^{3} + x^{2} y^{2} + x y + 1)

= (x y - 1) (x^{4} y^{4} + x^{3} y^{3} + x^{2} y^{2} + x y + 1)

tan^{2} (θ) - 3 tan (θ) + 2

E (0.4)

f (y) = y e^{2}

0.2 j + 0.6 (f)

e^{t} sin (t) + e^{t} cos (t)

What is factor (x^5y^5)-1 ?
The solution to factor (x^5y^5)-1 is (xy-1)(x^4y^4+x^3y^3+x^2y^2+xy+1)