Factorise: $16 {(2 x - 1)}^{2} - 25 y^{2}$

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Solution

$16 {(2 x - 1)}^{2} - 25 y^{2}$
$= {(4 (2 x - 1))}^{2} - 25 y^{2}$
$= {(8 x - 4)}^{2} - {(5 y)}^{2}$
$= (8 x - 4 + 5 y) (8 x - 4 - 5 y)$
$= (8 x + 5 y - 4) (8 x - 5 y - 4)$

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