Answer :

To show: that the coefficient of x4 in the expansion of (1 + 2x + x2)5 is 212.


Formula Used:


We have,


(1 + 2x + x2)5=(1 +x+ x+ x2)5


=(1 +x+ x(1+x))5


=(1 +x)5(1 +x)5


=(1 +x)10


General term, Tr+1 of binomial expansionis given by,


Tr+1 nCr xn-r yr where s


nCr


Now, finding the general term,


Tr+110Cr


10-r=4


r=6


Thus, the coefficient of x4 in the expansion of (1 + 2x + x2)5 is given by,


10C4


10C4


10C4=210


Thus, the coefficient of x4 in the expansion of (1 + 2x + x2)5 is 210


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