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Popular >

expand 16(s+s')^{12}

Solution

expand

16 (s + s^{'})^{12}

Solution

16 s^{12} + 192 s^{11} s' + 1056 s^{10} (s')^{2} + 3520 s^{9} (s')^{3} + 7920 s^{8} (s')^{4} + 12672 s^{7} (s')^{5} + 14784 s^{6} (s')^{6} + 12672 s^{5} (s')^{7} + 7920 s^{4} (s')^{8} + 3520 s^{3} (s')^{9} + 1056 s^{2} (s')^{10} + 192 s (s')^{11} + 16 (s')^{12}

Solution steps

16 (s + s^{'})^{12}

(s + s^{'})^{12} = s^{12} + 12 s^{11} s^{'} + 66 s^{10} (s^{'})^{2} + 220 s^{9} (s^{'})^{3} + 495 s^{8} (s^{'})^{4} + 792 s^{7} (s^{'})^{5} + 924 s^{6} (s^{'})^{6} + 792 s^{5} (s^{'})^{7} + 495 s^{4} (s^{'})^{8} + 220 s^{3} (s^{'})^{9} + 66 s^{2} (s^{'})^{10} + 12 s (s^{'})^{11} + (s^{'})^{12}

= 16 (s^{12} + 12 s^{11} s^{^{'}} + 66 s^{10} (s^{^{'}})^{2} + 220 s^{9} (s^{^{'}})^{3} + 495 s^{8} (s^{^{'}})^{4} + 792 s^{7} (s^{^{'}})^{5} + 924 s^{6} (s^{^{'}})^{6} + 792 s^{5} (s^{^{'}})^{7} + 495 s^{4} (s^{^{'}})^{8} + 220 s^{3} (s^{^{'}})^{9} + 66 s^{2} (s^{^{'}})^{10} + 12 s (s^{^{'}})^{11} + (s^{^{'}})^{12})

Distribute parentheses

= 16 s^{12} + 16 \cdot 12 s^{11} s^{^{'}} + 16 \cdot 66 s^{10} (s^{^{'}})^{2} + 16 \cdot 220 s^{9} (s^{^{'}})^{3} + 16 \cdot 495 s^{8} (s^{^{'}})^{4} + 16 \cdot 792 s^{7} (s^{^{'}})^{5} + 16 \cdot 924 s^{6} (s^{^{'}})^{6} + 16 \cdot 792 s^{5} (s^{^{'}})^{7} + 16 \cdot 495 s^{4} (s^{^{'}})^{8} + 16 \cdot 220 s^{3} (s^{^{'}})^{9} + 16 \cdot 66 s^{2} (s^{^{'}})^{10} + 16 \cdot 12 s (s^{^{'}})^{11} + 16 (s^{^{'}})^{12}

Simplify

16 s^{12} + 16 \cdot 12 s^{11} s^{'} + 16 \cdot 66 s^{10} (s^{'})^{2} + 16 \cdot 220 s^{9} (s^{'})^{3} + 16 \cdot 495 s^{8} (s^{'})^{4} + 16 \cdot 792 s^{7} (s^{'})^{5} + 16 \cdot 924 s^{6} (s^{'})^{6} + 16 \cdot 792 s^{5} (s^{'})^{7} + 16 \cdot 495 s^{4} (s^{'})^{8} + 16 \cdot 220 s^{3} (s^{'})^{9} + 16 \cdot 66 s^{2} (s^{'})^{10} + 16 \cdot 12 s (s^{'})^{11} + 16 (s^{'})^{12} : 16 s^{12} + 192 s^{11} s^{'} + 1056 s^{10} (s^{'})^{2} + 3520 s^{9} (s^{'})^{3} + 7920 s^{8} (s^{'})^{4} + 12672 s^{7} (s^{'})^{5} + 14784 s^{6} (s^{'})^{6} + 12672 s^{5} (s^{'})^{7} + 7920 s^{4} (s^{'})^{8} + 3520 s^{3} (s^{'})^{9} + 1056 s^{2} (s^{'})^{10} + 192 s (s^{'})^{11} + 16 (s^{'})^{12}

= 16 s^{12} + 192 s^{11} s^{'} + 1056 s^{10} (s^{'})^{2} + 3520 s^{9} (s^{'})^{3} + 7920 s^{8} (s^{'})^{4} + 12672 s^{7} (s^{'})^{5} + 14784 s^{6} (s^{'})^{6} + 12672 s^{5} (s^{'})^{7} + 7920 s^{4} (s^{'})^{8} + 3520 s^{3} (s^{'})^{9} + 1056 s^{2} (s^{'})^{10} + 192 s (s^{'})^{11} + 16 (s^{'})^{12}

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Frequently Asked Questions (FAQ)

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