Question

Find the no of terms in the expansion of (√x+√y)^8+(√x-√y)^8​

Answer 1

Answer:

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Answer 2

The number of terms in the expansion is 5.

Step-by-step explanation:

The binomial expansion of $(\sqrt{x} + \sqrt{y})^{8}$ is given as follows:

$(\sqrt{x} + \sqrt{y})^{8} = (\sqrt{x} )^{8} + ^8C_{1}(\sqrt{x} )^{7}(\sqrt{y} )^{1} + ^8C_{2}(\sqrt{x} )^{6}(\sqrt{y} )^{2} + ........... + ^8C_{8}(\sqrt{y} )^{8}$ ......... (1)

Again, the binomial expansion of $(\sqrt{x} - \sqrt{y})^{8}$ is given as follows:

$(\sqrt{x} - \sqrt{y})^{8} = (\sqrt{x} )^{8} - ^8C_{1}(\sqrt{x} )^{7}(\sqrt{y} )^{1} + ^8C_{2}(\sqrt{x} )^{6}(\sqrt{y} )^{2} + ........... + ^8C_{8}(\sqrt{y} )^{8}$ ......... (2)

Therefore, adding equations (1) and (2) we get,

$(\sqrt{x} + \sqrt{y})^{8} + (\sqrt{x} - \sqrt{y})^{8} = 2 \times (\sqrt{x} )^{8} + 2\times ^8C_{2}(\sqrt{x} )^{6}(\sqrt{y} )^{2} + ........... + 2 \times ^8C_{8}(\sqrt{y} )^{8}$

Hence, the number of terms in the expansion is 5. (Answer)