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Popular >

expand 96(s+s')^{10}

Solution

expand

96 (s + s^{'})^{10}

Solution

96 s^{10} + 960 s^{9} s' + 4320 s^{8} (s')^{2} + 11520 s^{7} (s')^{3} + 20160 s^{6} (s')^{4} + 24192 s^{5} (s')^{5} + 20160 s^{4} (s')^{6} + 11520 s^{3} (s')^{7} + 4320 s^{2} (s')^{8} + 960 s (s')^{9} + 96 (s')^{10}

Solution steps

96 (s + s^{'})^{10}

(s + s^{'})^{10} = s^{10} + 10 s^{9} s^{'} + 45 s^{8} (s^{'})^{2} + 120 s^{7} (s^{'})^{3} + 210 s^{6} (s^{'})^{4} + 252 s^{5} (s^{'})^{5} + 210 s^{4} (s^{'})^{6} + 120 s^{3} (s^{'})^{7} + 45 s^{2} (s^{'})^{8} + 10 s (s^{'})^{9} + (s^{'})^{10}

= 96 (s^{10} + 10 s^{9} s^{^{'}} + 45 s^{8} (s^{^{'}})^{2} + 120 s^{7} (s^{^{'}})^{3} + 210 s^{6} (s^{^{'}})^{4} + 252 s^{5} (s^{^{'}})^{5} + 210 s^{4} (s^{^{'}})^{6} + 120 s^{3} (s^{^{'}})^{7} + 45 s^{2} (s^{^{'}})^{8} + 10 s (s^{^{'}})^{9} + (s^{^{'}})^{10})

Distribute parentheses

= 96 s^{10} + 96 \cdot 10 s^{9} s^{^{'}} + 96 \cdot 45 s^{8} (s^{^{'}})^{2} + 96 \cdot 120 s^{7} (s^{^{'}})^{3} + 96 \cdot 210 s^{6} (s^{^{'}})^{4} + 96 \cdot 252 s^{5} (s^{^{'}})^{5} + 96 \cdot 210 s^{4} (s^{^{'}})^{6} + 96 \cdot 120 s^{3} (s^{^{'}})^{7} + 96 \cdot 45 s^{2} (s^{^{'}})^{8} + 96 \cdot 10 s (s^{^{'}})^{9} + 96 (s^{^{'}})^{10}

Simplify

96 s^{10} + 96 \cdot 10 s^{9} s^{'} + 96 \cdot 45 s^{8} (s^{'})^{2} + 96 \cdot 120 s^{7} (s^{'})^{3} + 96 \cdot 210 s^{6} (s^{'})^{4} + 96 \cdot 252 s^{5} (s^{'})^{5} + 96 \cdot 210 s^{4} (s^{'})^{6} + 96 \cdot 120 s^{3} (s^{'})^{7} + 96 \cdot 45 s^{2} (s^{'})^{8} + 96 \cdot 10 s (s^{'})^{9} + 96 (s^{'})^{10} : 96 s^{10} + 960 s^{9} s^{'} + 4320 s^{8} (s^{'})^{2} + 11520 s^{7} (s^{'})^{3} + 20160 s^{6} (s^{'})^{4} + 24192 s^{5} (s^{'})^{5} + 20160 s^{4} (s^{'})^{6} + 11520 s^{3} (s^{'})^{7} + 4320 s^{2} (s^{'})^{8} + 960 s (s^{'})^{9} + 96 (s^{'})^{10}

= 96 s^{10} + 960 s^{9} s^{'} + 4320 s^{8} (s^{'})^{2} + 11520 s^{7} (s^{'})^{3} + 20160 s^{6} (s^{'})^{4} + 24192 s^{5} (s^{'})^{5} + 20160 s^{4} (s^{'})^{6} + 11520 s^{3} (s^{'})^{7} + 4320 s^{2} (s^{'})^{8} + 960 s (s^{'})^{9} + 96 (s^{'})^{10}

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