Factorise: $25 m^{2} - 40 m n + 16 n^{2}$

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Solution

Using the identity $(a^{2} + b^{2} - 2 a b) = (a - b)^{2}$
We can write it as $(25 m^{2} + 16 n^{2} - 40 m n)$ as
$= (5 m)^{2} + (4 n)^{2} - 2 \times 5 m \times 4 n$
$= (5 m - 4 n)^{2}$
Hence, the factors are $(5 m - 4 n) (5 m - 4 n)$ .

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