The number of non-zero terms in the expansion | vedclass

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(C) The expansion of $(a + b)^n + (a - b)^n$ is given by $2[\binom{n}{0}a^n + \binom{n}{2}a^{n-2}b^2 + \binom{n}{4}a^{n-4}b^4 + \dots]$.Here,$a = 1$,$

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$5$

Vedclass · Answer

(C) The expansion of $(a + b)^n + (a - b)^n$ is given by $2[\binom{n}{0}a^n + \binom{n}{2}a^{n-2}b^2 + \binom{n}{4}a^{n-4}b^4 + \dots]$.Here,$a = 1$,$b = 3\sqrt{2}x$,and $n = 9$.Substituting these values,the expression becomes $2[\binom{9}{0}(1)^9 + \binom{9}{2}(1)^7(3\sqrt{2}x)^2 + \binom{9}{4}(1)^5(3\sqrt{2}x)^4 + \binom{9}{6}(1)^3(3\sqrt{2}x)^6 + \binom{9}{8}(1)^1(3\sqrt{2}x)^8]$.This results in $2[1 + 36(18x^2) + 126(324x^4) + 84(5832x^6) + 9(104976x^8)]$.Since all coefficients are non-zero,there are $5$ terms in the expansion.

The number of non-zero terms in the expansion of $(1 + 3\sqrt{2}x)^9 + (1 - 3\sqrt{2}x)^9$ is

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