What is expand (9cos(x)-9cos(9x))^2 ?

The solution to expand (9cos(x)-9cos(9x))^2 is 81cos^2(x)-162cos(x)cos(9x)+81cos^2(9x)

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expand (9cos(x)-9cos(9x))^2

expand

(9 cos (x) - 9 cos (9 x))^{2}

81 cos^{2} (x) - 162 cos (x) cos (9 x) + 81 cos^{2} (9 x)

Solution steps

(9 cos (x) - 9 cos (9 x))^{2}

Apply Perfect Square Formula:

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

(9 cos (x) - 9 cos (9 x))^{2} = (9 cos (x))^{2} - 2 \cdot 9 cos (x) \cdot 9 cos (9 x) + (9 cos (9 x))^{2}

= (9 cos (x))^{2} - 2 \cdot 9 cos (x) \cdot 9 cos (9 x) + (9 cos (9 x))^{2}

Simplify

(9 cos (x))^{2} - 2 \cdot 9 cos (x) \cdot 9 cos (9 x) + (9 cos (9 x))^{2} : 81 cos^{2} (x) - 162 cos (x) cos (9 x) + 81 cos^{2} (9 x)

= 81 cos^{2} (x) - 162 cos (x) cos (9 x) + 81 cos^{2} (9 x)

\frac{( 7 s ^{2} + 23 s + 30 )}{( s - 2 ) ( s ^{2} + 2 s + 5 )}

- 3 (1 + \frac{i}{n})^{2}

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

\frac{( x ^{2} + 14 x + 48 ) ( x + 6 )}{2}

\frac{20000 ( 1 - e ^{- s} )}{( s + 100 ) ^{2}}

What is expand (9cos(x)-9cos(9x))^2 ?
The solution to expand (9cos(x)-9cos(9x))^2 is 81cos^2(x)-162cos(x)cos(9x)+81cos^2(9x)