a) `3x^2- 6x`
= `3x.(x-2)`
b) `x^2-2x+1-y^2`
= `(x^2- 2x + 1) - y^2`
= `(x - 1)^2 - y^2`
= `(x - 1 - y)(x - 1 + y)`
c) `9x^3 - 9x^2y - 4x + 4y`
= `9x^2(x - y) - 4.(x - y)`
= `(x - y)(9x^ - 4)`
= `(x - y)(3x - 2)(3x + 2)`
d) `x^3- 2x^2 - 8x`
= `x^3- 4x^2+ 2x^2- 8x`
= `x^2.(x - 4) + 2x.(x - 4)`
= `(x^2+ 2x)(x - 4)`
= `x(x + 2)(x - 4)`
e) `4x^2 - 12xy + 5y^2`
= `4x^2 - 10xy - 2xy + 5y^2`
= `2x(2x - 5y) - y(2x - 5y)`
= `(2x - 5y)(2x - y)`
f) `(x + y + 2z)^2+ (x + y - z)^2- 9z^2`
= `(x + y + 2z)^2+ (x + y - z - 3z)(x + y - z + 3z)`
= `(x + y + 2z)^2+ (x + y - 4z)(x + y + 2z)`
= `(x + y + 2z)(x + y + 2z + x + y - 4z)`
= `(x + y + 2z)(2x + 2y - 2z)`
= `(x + y + 2z)(x + y - z)2`
g, `x^4+2019x^2+2018x+2019`
=`x^4 + 2019x^+ 2019x - x + 2019`
= `(x^4- x) + (2019x^2+ 2019x + 2019)`
= `x.(x^3- 1) + 2019.(x^2+ x + 1)`
= `x(x - 1)(x^2 + x + 1) + 2019(x^2+ x + 1)`
= `(x^2+ x + 1)(x^2- x + 2019)`
