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

The solution to expand (3x^2-3)^3 is 27x^6-81x^4+81x^2-27

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expand (3x^2-3)^3

expand

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

27 x^{6} - 81 x^{4} + 81 x^{2} - 27

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 x^{2})^{3} - 3 (3 x^{2})^{2} \cdot 3 + 3 \cdot 3 x^{2} \cdot 3^{2} - 3^{3} : 27 x^{6} - 81 x^{4} + 81 x^{2} - 27

= 27 x^{6} - 81 x^{4} + 81 x^{2} - 27

6 (6 + 10)

(3 + 2 x - 5 x^{2}) (2 - 3 x + 5 x^{2})

(1 - 4 x)^{3} - 2

43 (25 + 62)

\frac{5}{6} + \frac{1}{7}

What is expand (3x^2-3)^3 ?
The solution to expand (3x^2-3)^3 is 27x^6-81x^4+81x^2-27