What is factor ax^3+by^3+bx^3+ay^3 ?

The solution to factor ax^3+by^3+bx^3+ay^3 is (x^2+y^2-xy)(x+y)(a+b)

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factor ax^3+by^3+bx^3+ay^3

factor

a x^{3} + b y^{3} + b x^{3} + a y^{3}

(x^{2} + y^{2} - x y) (x + y) (a + b)

Solution steps

a x^{3} + b y^{3} + b x^{3} + a y^{3}

Factor out common term

a

= a (x^{3} + y^{3}) + b y^{3} + b x^{3}

Factor

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

= a (x + y) (x^{2} - x y + y^{2}) + b y^{3} + b x^{3}

Factor out common term

b

= a (x + y) (x^{2} + y^{2} - x y) + b (y^{3} + x^{3})

Factor

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

= a (x + y) (x^{2} - x y + y^{2}) + b (x + y) (x^{2} - x y + y^{2})

Factor out common term

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

= (x^{2} + y^{2} - x y) (x + y) (a + b)

y^{2} - 3 y - 4

\frac{4}{5} - \frac{3}{10} m = \frac{1}{10} m - \frac{4}{5}

x^{2} = 10 x + 14

8 + \frac{5}{2}

u^{2} = 10 u

What is factor ax^3+by^3+bx^3+ay^3 ?
The solution to factor ax^3+by^3+bx^3+ay^3 is (x^2+y^2-xy)(x+y)(a+b)