Factorise:
$4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y + 30 y z + 20 z x$

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Solution

Now,
$4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y + 30 y z + 20 z x$
Using identity $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$= (2 x)^{2} + (3 y)^{2} + (5 z)^{2} + 2 \times 2 x \times 3 y + 2 \times 3 y \times 5 z + 2 \times 2 x \times 5 z$
$= (2 x + 3 y + 5 z)^{2}$
$∴ 4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y + 30 y z + 20 z x = (2 x + 3 y + 5 z) (2 x + 3 y + 5 z)$

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