What is factor 125d^6a^3+216t^3e^9 ?

The solution to factor 125d^6a^3+216t^3e^9 is (5d^2a+6e^3t)(25d^4a^2-30e^3d^2at+36e^6t^2)

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factor 125d^6a^3+216t^3e^9

factor

125 d^{6} a^{3} + 216 t^{3} e^{9}

(5 d^{2} a + 6 e^{3} t) (25 d^{4} a^{2} - 30 e^{3} d^{2} a t + 36 e^{6} t^{2})

Solution steps

125 d^{6} a^{3} + 216 t^{3} e^{9}

Rewrite

125 d^{6} a^{3}

(5 d^{2} a)^{3}

Rewrite

216 t^{3} e^{9}

(6 t e^{3})^{3}

= (5 d^{2} a)^{3} + (6 t e^{3})^{3}

Apply Sum of Cubes Formula:

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

(5 d^{2} a)^{3} + (6 t e^{3})^{3} = (5 d^{2} a + 6 t e^{3}) ((5 d^{2} a)^{2} - 5 d^{2} a 6 t e^{3} + (6 t e^{3})^{2})

= (5 d^{2} a + 6 t e^{3}) ((5 d^{2} a)^{2} - 5 d^{2} a 6 t e^{3} + (6 t e^{3})^{2})

Simplify

(5 d^{2} a + 6 t e^{3}) ((5 d^{2} a)^{2} - 5 d^{2} a \cdot 6 t e^{3} + (6 t e^{3})^{2}) : (5 d^{2} a + 6 e^{3} t) (25 d^{4} a^{2} - 30 e^{3} d^{2} a t + 36 e^{6} t^{2})

= (5 d^{2} a + 6 e^{3} t) (25 d^{4} a^{2} - 30 e^{3} d^{2} a t + 36 e^{6} t^{2})

2 cos^{2} (x) + 3 cos (x) - 2

25 e^{2} - 16

8^{2} + 8 x - 6

(sin (3 x))^{2}

(\frac{d y}{d x})^{4}

What is factor 125d^6a^3+216t^3e^9 ?
The solution to factor 125d^6a^3+216t^3e^9 is (5d^2a+6e^3t)(25d^4a^2-30e^3d^2at+36e^6t^2)