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Popular >

expand (1+x^4+x^6)^7

Solution

expand

(1 + x^{4} + x^{6})^{7}

Solution

x^{42} + 7 x^{40} + 21 x^{38} + 42 x^{36} + 77 x^{34} + 126 x^{32} + 168 x^{30} + 211 x^{28} + 252 x^{26} + 252 x^{24} + 245 x^{22} + 231 x^{20} + 175 x^{18} + 140 x^{16} + 105 x^{14} + 56 x^{12} + 42 x^{10} + 21 x^{8} + 7 x^{6} + 7 x^{4} + 1

Solution steps

(1 + x^{4} + x^{6})^{7}

(1 + x^{4} + x^{6})^{7} = (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6})

= (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1) (x^{6} + x^{4} + 1)

Expand

(1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) (1 + x^{4} + x^{6}) : x^{42} + 7 x^{40} + 21 x^{38} + 42 x^{36} + 77 x^{34} + 126 x^{32} + 168 x^{30} + 211 x^{28} + 252 x^{26} + 252 x^{24} + 245 x^{22} + 231 x^{20} + 175 x^{18} + 140 x^{16} + 105 x^{14} + 56 x^{12} + 42 x^{10} + 21 x^{8} + 7 x^{6} + 7 x^{4} + 1

= x^{42} + 7 x^{40} + 21 x^{38} + 42 x^{36} + 77 x^{34} + 126 x^{32} + 168 x^{30} + 211 x^{28} + 252 x^{26} + 252 x^{24} + 245 x^{22} + 231 x^{20} + 175 x^{18} + 140 x^{16} + 105 x^{14} + 56 x^{12} + 42 x^{10} + 21 x^{8} + 7 x^{6} + 7 x^{4} + 1

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Frequently Asked Questions (FAQ)

What is expand (1+x^4+x^6)^7 ?
The solution to expand (1+x^4+x^6)^7 is