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The total number of terms in the expansion of $(x+y)^{60}+(x-y)^{60}$ is
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Verified Answer
The correct answer is:
31
$\begin{aligned}(x+y)^{60}={ }^{60} C_0 x^{60}-{ }^{60} C_1 x^{59} y+\ldots . . & \\ & +{ }^{60} C_{60} y^{60} \ldots(\mathrm{i})\end{aligned}$
By adding Eq. (i) and Eq. (ii)
$\begin{aligned}
& (x+y)^{60}+(x-y)^{60} \\
& =\underbrace{2\left({ }^{60} C_0 x^6+{ }^{60} C_2 x^{58} y^2+\ldots+{ }^{60} C_{60} y^{60}\right)}_{31 \text { terms }}
\end{aligned}$
Hence, the expansion of $(x+y)^{60}+(x-y)^{60}$ has 31 terms.
By adding Eq. (i) and Eq. (ii)
$\begin{aligned}
& (x+y)^{60}+(x-y)^{60} \\
& =\underbrace{2\left({ }^{60} C_0 x^6+{ }^{60} C_2 x^{58} y^2+\ldots+{ }^{60} C_{60} y^{60}\right)}_{31 \text { terms }}
\end{aligned}$
Hence, the expansion of $(x+y)^{60}+(x-y)^{60}$ has 31 terms.
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