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Popular >

expand-1008(s+s')^7

Solution

expand

- 1008 (s + s^{'})^{7}

Solution

- 1008 s^{7} - 7056 s^{6} s' - 21168 s^{5} (s')^{2} - 35280 s^{4} (s')^{3} - 35280 s^{3} (s')^{4} - 21168 s^{2} (s')^{5} - 7056 s (s')^{6} - 1008 (s')^{7}

Solution steps

- 1008 (s + s^{'})^{7}

(s + s^{'})^{7} = s^{7} + 7 s^{6} s^{'} + 21 s^{5} (s^{'})^{2} + 35 s^{4} (s^{'})^{3} + 35 s^{3} (s^{'})^{4} + 21 s^{2} (s^{'})^{5} + 7 s (s^{'})^{6} + (s^{'})^{7}

= - 1008 (s^{7} + 7 s^{6} s^{^{'}} + 21 s^{5} (s^{^{'}})^{2} + 35 s^{4} (s^{^{'}})^{3} + 35 s^{3} (s^{^{'}})^{4} + 21 s^{2} (s^{^{'}})^{5} + 7 s (s^{^{'}})^{6} + (s^{^{'}})^{7})

Distribute parentheses

= (- 1008) s^{7} + (- 1008) \cdot 7 s^{6} s^{^{'}} + (- 1008) \cdot 21 s^{5} (s^{^{'}})^{2} + (- 1008) \cdot 35 s^{4} (s^{^{'}})^{3} + (- 1008) \cdot 35 s^{3} (s^{^{'}})^{4} + (- 1008) \cdot 21 s^{2} (s^{^{'}})^{5} + (- 1008) \cdot 7 s (s^{^{'}})^{6} + (- 1008) (s^{^{'}})^{7}

Apply minus-plus rules

+ (- a) = - a

= - 1008 s^{7} - 1008 \cdot 7 s^{6} s^{^{'}} - 1008 \cdot 21 s^{5} (s^{^{'}})^{2} - 1008 \cdot 35 s^{4} (s^{^{'}})^{3} - 1008 \cdot 35 s^{3} (s^{^{'}})^{4} - 1008 \cdot 21 s^{2} (s^{^{'}})^{5} - 1008 \cdot 7 s (s^{^{'}})^{6} - 1008 (s^{^{'}})^{7}

Simplify

- 1008 s^{7} - 1008 \cdot 7 s^{6} s^{'} - 1008 \cdot 21 s^{5} (s^{'})^{2} - 1008 \cdot 35 s^{4} (s^{'})^{3} - 1008 \cdot 35 s^{3} (s^{'})^{4} - 1008 \cdot 21 s^{2} (s^{'})^{5} - 1008 \cdot 7 s (s^{'})^{6} - 1008 (s^{'})^{7} : - 1008 s^{7} - 7056 s^{6} s^{'} - 21168 s^{5} (s^{'})^{2} - 35280 s^{4} (s^{'})^{3} - 35280 s^{3} (s^{'})^{4} - 21168 s^{2} (s^{'})^{5} - 7056 s (s^{'})^{6} - 1008 (s^{'})^{7}

= - 1008 s^{7} - 7056 s^{6} s^{'} - 21168 s^{5} (s^{'})^{2} - 35280 s^{4} (s^{'})^{3} - 35280 s^{3} (s^{'})^{4} - 21168 s^{2} (s^{'})^{5} - 7056 s (s^{'})^{6} - 1008 (s^{'})^{7}

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Frequently Asked Questions (FAQ)

What is expand-1008(s+s')^7 ?
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