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

The solution to expand (3x^2-2y)^3 is 27x^6-54x^4y+36x^2y^2-8y^3

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

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

2.82

\frac{6 x ^{3} + 13 x ^{2} - 5 x}{4 x ^{2} - 25}

sec (x) tan (x) + sec^{2} (x)

(y^{2} - 6 y + 10)^{2}

(1 - sin^{2} (x)) (1 + tan^{2} (x))

What is expand (3x^2-2y)^3 ?
The solution to expand (3x^2-2y)^3 is 27x^6-54x^4y+36x^2y^2-8y^3