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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}

Apply minus-plus rules

+ (- a) = - a

= - 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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Frequently Asked Questions (FAQ)

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