Factorise the following:
$25 x^{2}+16 y^{2}+4 z^{2}-40 x y+16 y z-20 x z$
$25 x^{2}+16 y^{2}+4 z^{2}-40 x y+16 y z-20 x z$
(N/A) The given expression is $25 x^{2}+16 y^{2}+4 z^{2}-40 x y+16 y z-20 x z$.
We use the algebraic identity: $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$.
Comparing the given expression with the identity,we can rewrite it as:
$=(-5 x)^{2}+(4 y)^{2}+(2 z)^{2}+2(-5 x)(4 y)+2(4 y)(2 z)+2(2 z)(-5 x)$.
Here,$a = -5x$,$b = 4y$,and $c = 2z$.
Therefore,the expression simplifies to $(-5 x+4 y+2 z)^{2}$ or $(5 x-4 y-2 z)^{2}$.
We use the algebraic identity: $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$.
Comparing the given expression with the identity,we can rewrite it as:
$=(-5 x)^{2}+(4 y)^{2}+(2 z)^{2}+2(-5 x)(4 y)+2(4 y)(2 z)+2(2 z)(-5 x)$.
Here,$a = -5x$,$b = 4y$,and $c = 2z$.
Therefore,the expression simplifies to $(-5 x+4 y+2 z)^{2}$ or $(5 x-4 y-2 z)^{2}$.
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