1.

Factorise `x^(2)-6x-y^(2)+9`.

Answer» Given expression : `x^(2)-6x-y^(2)+9`
Here, `x^(2)-6x+9` is perfect square.
`therefore` By shifting the position of terms
`x^(2)-6x-y^(2)+9=(x^(2)-6x+9)-y^(2)`
`=(x-3)^(2)-(y)^(2) [because x^(2)-6x+9=(x)^(2)-2(x)(3)+(3)^(2)]`
=(x-3+y)(x-3-y)=(x+y-3)(x-y-3)


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