a: \(3xy-9x^2\)
\(=3x\cdot y-3x\cdot3x\)
\(=3x\left(y-3x\right)\)
b: \(25-x^2+2xy-y^2\)
\(=25-\left(x^2-2xy+y^2\right)\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(5-x+y\right)\left(5+x-y\right)\)
c: \(x^3-3x^2-4x+12\)
\(=x^2\cdot\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-4\right)\)
\(=\left(x-3\right)\left(x-2\right)\left(x+2\right)\)
d: \(x^2-5x+6\)
\(=x^2-2x-3x+6\)
\(=x\cdot\left(x-2\right)-3\left(x-2\right)=\left(x-2\right)\left(x-3\right)\)
a) \(3xy-9x^2\)
\(=3x\left(y-3x\right)\)
b) \(25-x^2+2xy-y^2\)
\(=5^2-\left(x^2-2xy+y^2\right)\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(5+x-y\right)\left(5-x+y\right)\)
c) \(x^3-3x^2-4x+12\)
\(=x^2\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x^2-4\right)\left(x-3\right)\)
\(=\left(x+2\right)\left(x-2\right)\left(x-3\right)\)
d) \(x^2-5x+6\)
\(=x^2-2x-3x+6\)
\(=x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x-2\right)\left(x-3\right)\)
`3xy-9x^2`
`=3x(y-3x)`
`25-x^2+2xy-y^2`
`=25-(x^2-2xy+y^2)`
`= 25-(x-y)^2`
`=(5-x+y)(5+x+y)`
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`x^3-3x^2-4x+12`
`=(x^3-3x^2)-(4x-12)`
`= x^2(x-3)-4(x-3)`
`=(x-3)(x^2-4)`
`=(x-3)(x-2)(x+2)`
`x^2-5x+6`
`=x^2-2x-3x+6`
`= x(x-2)-3(x-2)`
`=(x-2)(x-3)`
