# Show that the coefficient of x4 in the expansion of (1 + 2x + x2)5 is 212.

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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