Expand $(x^{2} + 2 a)^{5}$ by binomial theorem.

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Solution

$(x^{2} + 2 a)^{5}$
$\Rightarrow^{5} C_{0} (x^{2})^{5} +^{5} C_{1} (x^{2})^{4} (2 a) +^{5} C_{3} (x^{2})^{3} (2 a)^{2} +^{5} C_{2} (x^{2})^{2} (2 a)^{3} +^{5} C_{4} (x^{2}) (2 a)^{4} +^{5} C_{5} (2 a)^{5}$

$\Rightarrow x^{10} + 5 \times 2 a x^{8} + 10 \times 4 a^{2} x^{6} + 10 \times 8 a^{3} x^{4} + 5 \times 16 a^{4} x^{2} + 32 a^{5} .$ $[S i n c e^{n} C_{r} = \frac{n!}{r! (n - r)!}]$

$\Rightarrow x^{10} + 10 a x^{8} + 40 a^{2} x^{6} + 80 a^{3} x^{4} + 80 a^{4} x^{2} + 32 a^{5} .$

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