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Popular >

expand (1+2x+x^2)^8

Solution

expand

(1 + 2 x + x^{2})^{8}

Solution

x^{16} + 16 x^{15} + 120 x^{14} + 560 x^{13} + 1820 x^{12} + 4368 x^{11} + 8008 x^{10} + 11440 x^{9} + 12870 x^{8} + 11440 x^{7} + 8008 x^{6} + 4368 x^{5} + 1820 x^{4} + 560 x^{3} + 120 x^{2} + 16 x + 1

Solution steps

(1 + 2 x + x^{2})^{8}

(1 + 2 x + x^{2})^{8} = (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2})

= (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1) (x^{2} + 2 x + 1)

Expand

(1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) (1 + 2 x + x^{2}) : x^{16} + 16 x^{15} + 120 x^{14} + 560 x^{13} + 1820 x^{12} + 4368 x^{11} + 8008 x^{10} + 11440 x^{9} + 12870 x^{8} + 11440 x^{7} + 8008 x^{6} + 4368 x^{5} + 1820 x^{4} + 560 x^{3} + 120 x^{2} + 16 x + 1

= x^{16} + 16 x^{15} + 120 x^{14} + 560 x^{13} + 1820 x^{12} + 4368 x^{11} + 8008 x^{10} + 11440 x^{9} + 12870 x^{8} + 11440 x^{7} + 8008 x^{6} + 4368 x^{5} + 1820 x^{4} + 560 x^{3} + 120 x^{2} + 16 x + 1

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Frequently Asked Questions (FAQ)

What is expand (1+2x+x^2)^8 ?
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