What is factor rs^3-27rt^3+3s^3-81t^3 ?

The solution to factor rs^3-27rt^3+3s^3-81t^3 is (s-3t)(s^2+9t^2+3st)(r+3)

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factor rs^3-27rt^3+3s^3-81t^3

factor

r s^{3} - 27 r t^{3} + 3 s^{3} - 81 t^{3}

(s - 3 t) (s^{2} + 9 t^{2} + 3 s t) (r + 3)

Solution steps

r s^{3} - 27 r t^{3} + 3 s^{3} - 81 t^{3}

Factor out common term

r

= r (s^{3} - 27 t^{3}) + 3 s^{3} - 81 t^{3}

Factor

s^{3} - 27 t^{3} : (s - 3 t) (s^{2} + 3 s t + 9 t^{2})

= r (s - 3 t) (s^{2} + 3 s t + 9 t^{2}) + 3 s^{3} - 81 t^{3}

Rewrite as

= r (s - 3 t) (s^{2} + t^{2} \cdot 9 + 3 s t) + 3 s^{3} - 3 \cdot 27 t^{3}

Factor out common term

3

= r (s - 3 t) (s^{2} + t^{2} \cdot 9 + 3 s t) + 3 (s^{3} - 27 t^{3})

Factor

s^{3} - 27 t^{3} : (s - 3 t) (s^{2} + 3 s t + 9 t^{2})

= r (s - 3 t) (s^{2} + 3 s t + 9 t^{2}) + 3 (s - 3 t) (s^{2} + 3 s t + 9 t^{2})

Factor out common term

(s - 3 t) (s^{2} + t^{2} \cdot 9 + 3 s t)

= (s - 3 t) (s^{2} + t^{2} \cdot 9 + 3 s t) (r + 3)

s im pl i f y \frac{g ^{8} h ^{2} m}{h g ^{7}}

- 6 (3 p - 3) = 90

s im pl i f y x (x^{2})

2 x^{2} - 12 x + 15 = 0

s im pl i f y 1 - (\frac{7}{25})^{2}

What is factor rs^3-27rt^3+3s^3-81t^3 ?
The solution to factor rs^3-27rt^3+3s^3-81t^3 is (s-3t)(s^2+9t^2+3st)(r+3)