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Finding Square Root through Prime Factorisation

Expand √1-4x...

Question

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$\sqrt{1 - 4 x^{2}}$

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Solution

$\begin{matrix} \sqrt{1 - 4 x^{2}} \Rightarrow \sqrt{1^{2} - {(2 x)}^{2}} [a^{2} - b^{2} = (a - b) (a + b)] \sqrt{(1 - 2 x) (1 + 2 x)} \end{matrix}$

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9 {(x + a)}^{2} - 4 x^{2}

Factorise:

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lim x \to \frac{1}{2} (\frac{8 x - 3}{2 x - 1} - \frac{4 x^{2} + 1}{4 x^{2} - 1})

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