(A) To expand $(x+3y-5z)^{2}$,we use the algebraic identity: $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$.Here,$a = x$,$b = 3y$,and $c = -5z$.Substit

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$x^{2}+9y^{2}+25z^{2}+6xy-30yz-10zx$

(A) To expand $(x+3y-5z)^{2}$,we use the algebraic identity: $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$.Here,$a = x$,$b = 3y$,and $c = -5z$.Substituting these values into the identity:$(x+3y-5z)^{2} = (x)^{2} + (3y)^{2} + (-5z)^{2} + 2(x)(3y) + 2(3y)(-5z) + 2(-5z)(x)$$= x^{2} + 9y^{2} + 25z^{2} + 6xy - 30yz - 10zx$.