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

The solution to expand (3x^4-x^2)^3 is 27x^{12}-27x^{10}+9x^8-x^6

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

expand

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

27 x^{12} - 27 x^{10} + 9 x^{8} - x^{6}

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(3 x^{4})^{3} - 3 (3 x^{4})^{2} x^{2} + 3 \cdot 3 x^{4} (x^{2})^{2} - (x^{2})^{3} : 27 x^{12} - 27 x^{10} + 9 x^{8} - x^{6}

= 27 x^{12} - 27 x^{10} + 9 x^{8} - x^{6}

6 - 18

(1 + 10 i)^{2}

4 + 12

12 x - 9 - 4 x + 3

9025

What is expand (3x^4-x^2)^3 ?
The solution to expand (3x^4-x^2)^3 is 27x^{12}-27x^{10}+9x^8-x^6