What is expand (2(x^2-2)^{16})/(15) ?

The solution to expand (2(x^2-2)^{16})/(15) is

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expand (2(x^2-2)^{16})/(15)

expand

\frac{2 ( x ^{2} - 2 ) ^{16}}{15}

\frac{2 x ^{32}}{15} - \frac{64 x ^{30}}{15} + 64 x^{28} - \frac{1792 x ^{26}}{3} + \frac{11648 x ^{24}}{3} - \frac{93184 x ^{22}}{5} + \frac{1025024 x ^{20}}{15} - \frac{585728 x ^{18}}{3} + 439296 x^{16} - \frac{2342912 x ^{14}}{3} + \frac{16400384 x ^{12}}{15} - \frac{5963776 x ^{10}}{5} + \frac{2981888 x ^{8}}{3} - \frac{1835008 x ^{6}}{3} + 262144 x^{4} - \frac{1048576 x ^{2}}{15} + \frac{131072}{15}

Solution steps

\frac{2 ( x ^{2} - 2 ) ^{16}}{15}

(x^{2} - 2)^{16} = x^{32} - 32 x^{30} + 480 x^{28} - 4480 x^{26} + 29120 x^{24} - 139776 x^{22} + 512512 x^{20} - 1464320 x^{18} + 3294720 x^{16} - 5857280 x^{14} + 8200192 x^{12} - 8945664 x^{10} + 7454720 x^{8} - 4587520 x^{6} + 1966080 x^{4} - 524288 x^{2} + 65536

= \frac{2 ( x ^{32} - 32 x ^{30} + 480 x ^{28} - 4480 x ^{26} + 29120 x ^{24} - 139776 x ^{22} + 512512 x ^{20} - 1464320 x ^{18} + 3294720 x ^{16} - 5857280 x ^{14} + 8200192 x ^{12} - 8945664 x ^{10} + 7454720 x ^{8} - 4587520 x ^{6} + 1966080 x ^{4} - 524288 x ^{2} + 65536 )}{15}

Expand

2 (x^{32} - 32 x^{30} + 480 x^{28} - 4480 x^{26} + 29120 x^{24} - 139776 x^{22} + 512512 x^{20} - 1464320 x^{18} + 3294720 x^{16} - 5857280 x^{14} + 8200192 x^{12} - 8945664 x^{10} + 7454720 x^{8} - 4587520 x^{6} + 1966080 x^{4} - 524288 x^{2} + 65536) : 2 x^{32} - 64 x^{30} + 960 x^{28} - 8960 x^{26} + 58240 x^{24} - 279552 x^{22} + 1025024 x^{20} - 2928640 x^{18} + 6589440 x^{16} - 11714560 x^{14} + 16400384 x^{12} - 17891328 x^{10} + 14909440 x^{8} - 9175040 x^{6} + 3932160 x^{4} - 1048576 x^{2} + 131072

= \frac{2 x ^{32} - 64 x ^{30} + 960 x ^{28} - 8960 x ^{26} + 58240 x ^{24} - 279552 x ^{22} + 1025024 x ^{20} - 2928640 x ^{18} + 6589440 x ^{16} - 11714560 x ^{14} + 16400384 x ^{12} - 17891328 x ^{10} + 14909440 x ^{8} - 9175040 x ^{6} + 3932160 x ^{4} - 1048576 x ^{2} + 131072}{15}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 x ^{32} - 64 x ^{30} + 960 x ^{28} - 8960 x ^{26} + 58240 x ^{24} - 279552 x ^{22} + 1025024 x ^{20} - 2928640 x ^{18} + 6589440 x ^{16} - 11714560 x ^{14} + 16400384 x ^{12} - 17891328 x ^{10} + 14909440 x ^{8} - 9175040 x ^{6} + 3932160 x ^{4} - 1048576 x ^{2} + 131072}{15} = \frac{2 x ^{32}}{15} - \frac{64 x ^{30}}{15} + \frac{960 x ^{28}}{15} - \frac{8960 x ^{26}}{15} + \frac{58240 x ^{24}}{15} - \frac{279552 x ^{22}}{15} + \frac{1025024 x ^{20}}{15} - \frac{2928640 x ^{18}}{15} + \frac{6589440 x ^{16}}{15} - \frac{11714560 x ^{14}}{15} + \frac{16400384 x ^{12}}{15} - \frac{17891328 x ^{10}}{15} + \frac{14909440 x ^{8}}{15} - \frac{9175040 x ^{6}}{15} + \frac{3932160 x ^{4}}{15} - \frac{1048576 x ^{2}}{15} + \frac{131072}{15}

= \frac{2 x ^{32}}{15} - \frac{64 x ^{30}}{15} + \frac{960 x ^{28}}{15} - \frac{8960 x ^{26}}{15} + \frac{58240 x ^{24}}{15} - \frac{279552 x ^{22}}{15} + \frac{1025024 x ^{20}}{15} - \frac{2928640 x ^{18}}{15} + \frac{6589440 x ^{16}}{15} - \frac{11714560 x ^{14}}{15} + \frac{16400384 x ^{12}}{15} - \frac{17891328 x ^{10}}{15} + \frac{14909440 x ^{8}}{15} - \frac{9175040 x ^{6}}{15} + \frac{3932160 x ^{4}}{15} - \frac{1048576 x ^{2}}{15} + \frac{131072}{15}

\frac{960 x ^{28}}{15} = 64 x^{28}

\frac{8960 x ^{26}}{15} = \frac{1792 x ^{26}}{3}

\frac{58240 x ^{24}}{15} = \frac{11648 x ^{24}}{3}

\frac{279552 x ^{22}}{15} = \frac{93184 x ^{22}}{5}

\frac{2928640 x ^{18}}{15} = \frac{585728 x ^{18}}{3}

\frac{6589440 x ^{16}}{15} = 439296 x^{16}

\frac{11714560 x ^{14}}{15} = \frac{2342912 x ^{14}}{3}

\frac{17891328 x ^{10}}{15} = \frac{5963776 x ^{10}}{5}

\frac{14909440 x ^{8}}{15} = \frac{2981888 x ^{8}}{3}

\frac{9175040 x ^{6}}{15} = \frac{1835008 x ^{6}}{3}

\frac{3932160 x ^{4}}{15} = 262144 x^{4}

= \frac{2 x ^{32}}{15} - \frac{64 x ^{30}}{15} + 64 x^{28} - \frac{1792 x ^{26}}{3} + \frac{11648 x ^{24}}{3} - \frac{93184 x ^{22}}{5} + \frac{1025024 x ^{20}}{15} - \frac{585728 x ^{18}}{3} + 439296 x^{16} - \frac{2342912 x ^{14}}{3} + \frac{16400384 x ^{12}}{15} - \frac{5963776 x ^{10}}{5} + \frac{2981888 x ^{8}}{3} - \frac{1835008 x ^{6}}{3} + 262144 x^{4} - \frac{1048576 x ^{2}}{15} + \frac{131072}{15}

\frac{sin ^{2} ( X ) ( cot ( X ) - csc ( X ) )}{cot ( X ) + csc ( X )} + 1

(1 + i 3)^{7}

x (\frac{1}{n ^{2}} + x^{2})

\frac{1}{( s + 1 ) ( s + 10 )}

(\frac{w L}{2} - w a) a

What is expand (2(x^2-2)^{16})/(15) ?
The solution to expand (2(x^2-2)^{16})/(15) is