What is expand (3x^3y-2z^4)^3 ?

The solution to expand (3x^3y-2z^4)^3 is 27x^9y^3-54x^6y^2z^4+36x^3yz^8-8z^{12}

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expand (3x^3y-2z^4)^3

expand

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

27 x^{9} y^{3} - 54 x^{6} y^{2} z^{4} + 36 x^{3} y z^{8} - 8 z^{12}

Solution steps

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

Apply Perfect Cube Formula:

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

(3 x^{3} y - 2 z^{4})^{3} = (3 x^{3} y)^{3} - 3 (3 x^{3} y)^{2} \cdot 2 z^{4} + 3 \cdot 3 x^{3} y (2 z^{4})^{2} - (2 z^{4})^{3}

= (3 x^{3} y)^{3} - 3 (3 x^{3} y)^{2} \cdot 2 z^{4} + 3 \cdot 3 x^{3} y (2 z^{4})^{2} - (2 z^{4})^{3}

Simplify

(3 x^{3} y)^{3} - 3 (3 x^{3} y)^{2} \cdot 2 z^{4} + 3 \cdot 3 x^{3} y (2 z^{4})^{2} - (2 z^{4})^{3} : 27 x^{9} y^{3} - 54 x^{6} y^{2} z^{4} + 36 x^{3} y z^{8} - 8 z^{12}

= 27 x^{9} y^{3} - 54 x^{6} y^{2} z^{4} + 36 x^{3} y z^{8} - 8 z^{12}

3 (\frac{7}{5} x + 4) - 2 (\frac{3}{2} - \frac{5}{4} x)

(x + 2) (x + 8)

(x + 2) (x + 9)

10 - 5 (9 n - 9)

2 tan (θ) (3 cos (θ))

What is expand (3x^3y-2z^4)^3 ?
The solution to expand (3x^3y-2z^4)^3 is 27x^9y^3-54x^6y^2z^4+36x^3yz^8-8z^{12}