`a)` `8x^4+12x^2y^4-16x^3y^4`
`=4x^2(2x^2+3y^2-4xy^4)`
`b)` `4xy^2+8xyz`
`=4xy(y^2+2z)`
`c)` `25(x-y)^2-16(x+y)^2`
`=[5(x-y)]^2-[4(x+y)]^2`
`=[5(x-y)-4(x+y)][5(x-y)+4(x+y)]`
`=(5x-5y-4x-4y)(5x-5y+4x+4y)`
`=(x-9y)(9x-y)`
`d)` `49(x-4)^2-9(x+2)^2`
`=[7(x-4)]^2-[3(x+2)]^2`
`=[7(x-4)-3(x+2)][7(x-4)+3(x+2)]`
`=(7x-28-3x-6)(7x-28+3x+6)`
`=(4x-34)(10x-22)`
`=2(2x-17)(10x-22)`
`e)` `x^4+x^3+x+1`
`=(x^4+x^3)+(x+1)`
`=x^3(x+1)+(x+1)`
`=(x+1)(x^3+1)`
`=(x+1)(x+1)(x^2-x+1)`
`=(x+1)^2(x^2-x+1)`
