c: \(x^3-xz^2-4x^2y+4xyz+4xyt-4xt^2\)
\(=x\left(x^2-z^2\right)-4xy\left(x-z\right)+4xt\left(y-t\right)\)
\(=x\left(x^2-z^2-4y\left(x-z\right)+4t\left(y-t\right)\right)\)
a: \(x^2+y^2-xz+2xy-yz\)
\(=\left(x^2+2xy+y^2\right)-z\left(x+y\right)\)
\(=\left(x+y\right)^2-z\left(x+y\right)=\left(x+y\right)\left(x+y-z\right)\)
b: \(12y^2-5y-2\)
\(=12y^2-8y+3y-2\)
\(=4y\left(3y-2\right)+\left(3y-2\right)\)
=(3y-2)(4y+1)
`a/`
`x^2 + y^2 - xz + 2xy - yz`
`= (x^2 + 2xy + y^2) - z(x + y)`
`= (x + y)^2 - z(x + y)`
`= (x + y)(x + y - z)`
`b/`
`12y^2 - 5y - 2 &= 12y^2 - 8y + 3y - 2`
`= 4y(3y - 2) + (3y - 2)`
`= (3y - 2)(4y + 1)`
`c/`
`x^3 - x^2z - 4x^2y + 4xyz + 4xyt - 4xt^2`
`= x(x^2 - z^2) - 4xy(x - z) + 4xt(y - t)`
`= x(x^2 - z^2 - 4y(x - z) + 4t(y - t))`
