What is factor mx^5+my^5+nx^5+ny^5 ?

The solution to factor mx^5+my^5+nx^5+ny^5 is (x^4+y^4+x^2y^2-x^3y-xy^3)(x+y)(m+n)

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factor mx^5+my^5+nx^5+ny^5

factor

m x^{5} + m y^{5} + n x^{5} + n y^{5}

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

Solution steps

m x^{5} + m y^{5} + n x^{5} + n y^{5}

Factor out common term

m

= m (x^{5} + y^{5}) + n x^{5} + n y^{5}

Factor

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

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

Factor out common term

n

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

Factor

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

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

Factor out common term

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

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

32 x^{4} y^{5}

\frac{3}{( 2 - 6 x ) ^{2}}

(18 x^{3}) + (- 13 x)

625 x^{2} + 150 x + 9 i z a r

f (x) = x^{2} - 3

What is factor mx^5+my^5+nx^5+ny^5 ?
The solution to factor mx^5+my^5+nx^5+ny^5 is (x^4+y^4+x^2y^2-x^3y-xy^3)(x+y)(m+n)