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Popular >

expand 216(s+s')^8

Solution

expand

216 (s + s^{'})^{8}

Solution

216 s^{8} + 1728 s^{7} s' + 6048 s^{6} (s')^{2} + 12096 s^{5} (s')^{3} + 15120 s^{4} (s')^{4} + 12096 s^{3} (s')^{5} + 6048 s^{2} (s')^{6} + 1728 s (s')^{7} + 216 (s')^{8}

Solution steps

216 (s + s^{'})^{8}

(s + s^{'})^{8} = s^{8} + 8 s^{7} s^{'} + 28 s^{6} (s^{'})^{2} + 56 s^{5} (s^{'})^{3} + 70 s^{4} (s^{'})^{4} + 56 s^{3} (s^{'})^{5} + 28 s^{2} (s^{'})^{6} + 8 s (s^{'})^{7} + (s^{'})^{8}

= 216 (s^{8} + 8 s^{7} s^{^{'}} + 28 s^{6} (s^{^{'}})^{2} + 56 s^{5} (s^{^{'}})^{3} + 70 s^{4} (s^{^{'}})^{4} + 56 s^{3} (s^{^{'}})^{5} + 28 s^{2} (s^{^{'}})^{6} + 8 s (s^{^{'}})^{7} + (s^{^{'}})^{8})

Distribute parentheses

= 216 s^{8} + 216 \cdot 8 s^{7} s^{^{'}} + 216 \cdot 28 s^{6} (s^{^{'}})^{2} + 216 \cdot 56 s^{5} (s^{^{'}})^{3} + 216 \cdot 70 s^{4} (s^{^{'}})^{4} + 216 \cdot 56 s^{3} (s^{^{'}})^{5} + 216 \cdot 28 s^{2} (s^{^{'}})^{6} + 216 \cdot 8 s (s^{^{'}})^{7} + 216 (s^{^{'}})^{8}

Simplify

216 s^{8} + 216 \cdot 8 s^{7} s^{'} + 216 \cdot 28 s^{6} (s^{'})^{2} + 216 \cdot 56 s^{5} (s^{'})^{3} + 216 \cdot 70 s^{4} (s^{'})^{4} + 216 \cdot 56 s^{3} (s^{'})^{5} + 216 \cdot 28 s^{2} (s^{'})^{6} + 216 \cdot 8 s (s^{'})^{7} + 216 (s^{'})^{8} : 216 s^{8} + 1728 s^{7} s^{'} + 6048 s^{6} (s^{'})^{2} + 12096 s^{5} (s^{'})^{3} + 15120 s^{4} (s^{'})^{4} + 12096 s^{3} (s^{'})^{5} + 6048 s^{2} (s^{'})^{6} + 1728 s (s^{'})^{7} + 216 (s^{'})^{8}

= 216 s^{8} + 1728 s^{7} s^{'} + 6048 s^{6} (s^{'})^{2} + 12096 s^{5} (s^{'})^{3} + 15120 s^{4} (s^{'})^{4} + 12096 s^{3} (s^{'})^{5} + 6048 s^{2} (s^{'})^{6} + 1728 s (s^{'})^{7} + 216 (s^{'})^{8}

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