Factorise $25 x^{2}+9 y^{2}+64+30 x y-48 y-80 x$.
(N/A) The given expression is $25 x^{2}+9 y^{2}+64+30 x y-48 y-80 x$.
This can be rewritten as $(5 x)^{2}+(3 y)^{2}+(-8)^{2}+2(5 x)(3 y)+2(3 y)(-8)+2(5 x)(-8)$.
This expression is in the form of the algebraic identity $a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a = (a+b+c)^{2}$.
Here,$a = 5 x$,$b = 3 y$,and $c = -8$.
Therefore,the expression becomes $(5 x+3 y-8)^{2}$,which is $(5 x+3 y-8)(5 x+3 y-8)$.
This can be rewritten as $(5 x)^{2}+(3 y)^{2}+(-8)^{2}+2(5 x)(3 y)+2(3 y)(-8)+2(5 x)(-8)$.
This expression is in the form of the algebraic identity $a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a = (a+b+c)^{2}$.
Here,$a = 5 x$,$b = 3 y$,and $c = -8$.
Therefore,the expression becomes $(5 x+3 y-8)^{2}$,which is $(5 x+3 y-8)(5 x+3 y-8)$.
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