Factorise $49 x^{2} - 112 x y + 64 y^{2}$

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Solution

Here $49 x^{2} - 112 x y + 64 y^{2}$ , we see that
$49 x^{2} = (7 x)^{2}, 64 y^{2} = (8 y)^{2}$ and $112 x y = 2 (7 x) (8 y)$
Thus comparing with Identity II,
$(x - y)^{2} \equiv x^{2} - 2 x y + y^{2}$ , we get
$49 x^{2} - 112 x y + 64 y^{2} = (7 x)^{2} - 2 (7 x) (8 y) + (8 y)^{2}$
$= (7 x - 8 y)^{2}$
$= (7 x - 8 y) (7 x - 8 y)$

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