`e) 5x^2-45y^2-30y-5`
`=5(x^2-9y^2-6y-1)`
`=5[x^2-(3y+1)^2]`
`=5(x-3y-1)(x+3y+1)`
`f)36-4x^2+20xy-25y^2`
`=36-(2x-5y)^2`
`=(6-2x+5y)(6+2x-5y)`
`g)5x-5y-x^2+2xy-y^2`
`=5(x-y)-(x-y)^2`
`=(x-y)(5-x+y)`
`h)x^3-3x+3x^2y+3xy^2+y^3-3y`
`=(x+y)^3-3(x+y)`
`=(x+y)[(x+y)^2-3]`
`=(x+y)(x+y-\sqrt{3})(x+y+\sqrt{3})`
e: \(5x^2-45y^2-30y-5\)
\(=5\left(x^2-9y^2-6y-1\right)\)
\(=5\left[x^2-\left(9y^2+6y+1\right)\right]\)
\(=5\left[x^2-\left(3y+1\right)^2\right]\)
\(=5\left(x-3y-1\right)\left(x+3y+1\right)\)
f: \(36-4x^2+20xy-25y^2\)
\(=6^2-\left(4x^2-20xy+25y^2\right)\)
\(=6^2-\left(2x-5y\right)^2=\left(6-2x+5y\right)\left(6+2x-5y\right)\)
g: \(5x-5y-x^2+2xy-y^2\)
\(=5\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=5\left(x-y\right)-\left(x-y\right)^2\)
=(x-y)(5-x+y)
h: \(x^3-3x+3x^2y+3xy^2+y^3-3y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-3\left(x+y\right)\)
\(=\left(x+y\right)^3-3\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-3\right]\)
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