Factorise: $25 x^{2} + 36 y^{2} + 49 z^{2} + 60 x y - 84 y z - 70 z x$

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Solution

$25 x^{2} + 36 y^{2} + 49 z^{2} + 60 x y - 84 y z - 70 z x$

Keeping $5 x = a,$ $6 y = b,$ $- 7 z = c$

We get, $a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a = (a + b + c)^{2}$

$\Rightarrow {(5 x + 6 y - 7 z)}^{2} .$

Hence, the answer is ${(5 x + 6 y - 7 z)}^{2}$

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Factorize the following algebraic expression: $25 x^{2} - 10 x + 1 - 36 y^{2}$

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