` \color{#0074D9}{#n}\color{#0088DD}{q}\color{#3399FF}{o}\color{#66AAFF}{c}\color{#99CCFF}{c} `

`1) 27x^4 - 8x `

`= x(27x^3 - 8) `

`= x[(3x)^3 - 2^3] `

`= x(3x-2)(9x^2 + 6x + 4) `

`2) 3x^3 - 18x^2 + 27x `

`=3x(x^2 - 6x + 9) `

`= 3x(x-3)^2 `

`3) 16x^2y - 4xy^2 - 4x^3 + x^2y`

`= (16x^2y + x^2y) - (4xy^2 + 4x^3) `

`= 17x^2y - 4x(y^2 + x^2) `

`= 17x^2y - 4xy^2 - 4x^3 `

`4) 2x^2 - 4xy + 2y^2 - 32`

`= (2x^2 - 4xy + 2y^2) - 32 `

`= 2(x^2 - 2xy + y^2) - 32 `

`= 2(x-y)^2 - 32 `

`= 2[(x-y)^2 - 16] `

`= 2[(x-y)^2 - 4^2] `

`= 2(x-y-4)(x-y+4) `

`5) 4x^2.(x+y) - x - y `

`= 4x^2(x+y) - (x+y) `

`= (4x^2-1)(x+y) `

`= (2x-1)(2x+1)(x+y)`

`6) 4a^2.(a-2ab) - 10a.(2b-a)`

`= 4a^3 - 8a^3b - 20ab + 10a^2 `

`= (4a^3 - 8a^3b) + (10a^2 - 20ab) `

`= 4a^3(1-2b) + 10a(a-2b) `

`= (a-2b)(4a^3 + 10a) `

`= (a-2b)(2a)(2a^2 + 5) `