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Addition and Subtraction of Algebraic Expression

Factorise the...

Question

Factorise the following expression-
$k^{4} + 4 k^{2} m^{2} + 4 m^{4}$

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Solution

$k^{4} + 4 k^{2} m^{2} + 4 m^{4}$
$= k^{4} + 2 k^{2} m^{2} + 2 k^{2} m^{2} + 4 m^{4}$
$= k^{2} (k^{2} + 2 m^{2}) + 2 m^{2} (k^{2} + 2 m^{2})$
$= (k^{2} + 2 m^{2}) (k^{2} + 2 m^{2})$
$= {(k^{2} + 2 m^{2})}^{2}$

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