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Sum of Binomial Coefficients with Alternate Signs

Expand the fo...

Question

Expand the following:

$(i i i) {(2 a + \frac{1}{2 a})}^{2}$

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Solution

Given: Expression is ${(2 a + \frac{1}{2 a})}^{2}$

Now, expand the given expression by using the sum of square identity $(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$\Rightarrow {(2 a + \frac{1}{2 a})}^{2} = (2 a)^{2} + {(\frac{1}{2 a})}^{2} + 2 \times 2 a \times \frac{1}{2 a}$

$= 4 a^{2} + \frac{1}{4 a^{2}} + 2$

Hence, expansion of ${(2 a + \frac{1}{2 a})}^{2}$ is $4 a^{2} + \frac{1}{4 a^{2}} + 2$

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Sum of Binomial Coefficients with Alternate Signs

Standard XII Mathematics

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