Find the number of terms in the expansions of the following: `(1+3sqrt(2)x)^9+(1-3sqrt(2)x)^9`

Explanation

`(1+3 sqrt{2} x)^{9}+(1-3 sqrt{2} x)^{9}`


Applying binomial theorem for expansion of the following


`=1+(3 sqrt{2} {x})(9_{C_1})+(3 sqrt{2} {x})^{2}(9_{C_2}) ldots({ }^9_{C_9}(3 sqrt{2} {x})^{9})
+1-(3 sqrt{2} {x})(9_{C_1})+(3 sqrt{2} {x})^{2}(9_{C_2}) ldots-(9_{C_9}(3 sqrt{2} {x})^{9}) `

`=2[1+(3 sqrt{2} {x})^{2}(9_{C_2})+(3 sqrt{2} {x}){ }^{4}(9_{C_4}) ldots(3 sqrt{2} {x})^{8}(9_{C_8})]`
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