Factorise: $36 x^{2} + 96 x y + 64 y^{2}$

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Solution

Using identity, $a^{2} + b^{2} - 2 a b = (a - b)^{2}$
$36 x^{2} + 96 x y + 64 y^{2} = (6 x)^{2} + 2 \times 6 x \times 8 y + (8 y)^{2}$
$= (6 x + 8 y)^{2}$
$= (6 x + 8 y) (6 x + 8 y)$
Hence, the factors are $(6 x + 8 y) (6 x + 8 y)$ .

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