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Popular >

expand (1+x+x^2)^9

Solution

expand

(1 + x + x^{2})^{9}

Solution

x^{18} + 9 x^{17} + 45 x^{16} + 156 x^{15} + 414 x^{14} + 882 x^{13} + 1554 x^{12} + 2304 x^{11} + 2907 x^{10} + 3139 x^{9} + 2907 x^{8} + 2304 x^{7} + 1554 x^{6} + 882 x^{5} + 414 x^{4} + 156 x^{3} + 45 x^{2} + 9 x + 1

Solution steps

(1 + x + x^{2})^{9}

(1 + x + x^{2})^{9} = (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2})

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

Expand

(1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) : x^{18} + 9 x^{17} + 45 x^{16} + 156 x^{15} + 414 x^{14} + 882 x^{13} + 1554 x^{12} + 2304 x^{11} + 2907 x^{10} + 3139 x^{9} + 2907 x^{8} + 2304 x^{7} + 1554 x^{6} + 882 x^{5} + 414 x^{4} + 156 x^{3} + 45 x^{2} + 9 x + 1

= x^{18} + 9 x^{17} + 45 x^{16} + 156 x^{15} + 414 x^{14} + 882 x^{13} + 1554 x^{12} + 2304 x^{11} + 2907 x^{10} + 3139 x^{9} + 2907 x^{8} + 2304 x^{7} + 1554 x^{6} + 882 x^{5} + 414 x^{4} + 156 x^{3} + 45 x^{2} + 9 x + 1

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Frequently Asked Questions (FAQ)

What is expand (1+x+x^2)^9 ?
The solution to expand (1+x+x^2)^9 is