What is expand (1-u^2)^3 ?

The solution to expand (1-u^2)^3 is 1-3u^2+3u^4-u^6

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expand (1-u^2)^3

expand

(1 - u^{2})^{3}

1 - 3 u^{2} + 3 u^{4} - u^{6}

Solution steps

(1 - u^{2})^{3}

Apply Perfect Cube Formula:

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

(1 - u^{2})^{3} = 1^{3} - 3 \cdot 1^{2} u^{2} + 3 \cdot 1 \cdot (u^{2})^{2} - (u^{2})^{3}

= 1^{3} - 3 \cdot 1^{2} u^{2} + 3 \cdot 1 \cdot (u^{2})^{2} - (u^{2})^{3}

Simplify

1^{3} - 3 \cdot 1^{2} u^{2} + 3 \cdot 1 \cdot (u^{2})^{2} - (u^{2})^{3} : 1 - 3 u^{2} + 3 u^{4} - u^{6}

= 1 - 3 u^{2} + 3 u^{4} - u^{6}

x^{\frac{1}{3}} \cdot x^{\frac{1}{3}} \cdot x^{\frac{1}{3}}

\frac{( 7 x ^{4} + 54 x ^{3} - 71 x ^{2} + 77 x - 117 )}{( x + 9 )}

\frac{\frac{3 x - 3}{28}}{\frac{x - 1}{7}}

(x - a)^{2} - b^{2}

\frac{sin ( θ )}{1 + sin ( θ )} - \frac{sin ( θ )}{1 - sin ( θ )}