What is factor 729u^3s^3-1000t^3 ?

The solution to factor 729u^3s^3-1000t^3 is (9us-10t)(81u^2s^2+90ust+100t^2)

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factor 729u^3s^3-1000t^3

factor

729 u^{3} s^{3} - 1000 t^{3}

(9 u s - 10 t) (81 u^{2} s^{2} + 90 u s t + 100 t^{2})

Solution steps

729 u^{3} s^{3} - 1000 t^{3}

Rewrite

729 u^{3} s^{3}

(3^{2} u s)^{3}

Rewrite

1000 t^{3}

(10 t)^{3}

= (3^{2} u s)^{3} - (10 t)^{3}

Apply Difference of Cubes Formula:

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

(3^{2} u s)^{3} - (10 t)^{3} = (3^{2} u s - 10 t) ((3^{2} u s)^{2} + 10 t 3^{2} u s + (10 t)^{2})

= (3^{2} u s - 10 t) ((10 t)^{2} + 10 t 3^{2} u s + (3^{2} u s)^{2})

Simplify

(3^{2} u s - 10 t) ((3^{2} u s)^{2} + 10 t \cdot 3^{2} u s + (10 t)^{2}) : (9 u s - 10 t) (81 u^{2} s^{2} + 90 u s t + 100 t^{2})

= (9 u s - 10 t) (81 u^{2} s^{2} + 90 u s t + 100 t^{2})

3 + 3 i

2 R e (z)

x^{3} + e x^{2} - π x

\frac{x + 5}{x ^{2} - 25}

e [x^{2}]

What is factor 729u^3s^3-1000t^3 ?
The solution to factor 729u^3s^3-1000t^3 is (9us-10t)(81u^2s^2+90ust+100t^2)