`a)x^4+64`
`=x^4+16x^2-16x^2+64`
`=(x^4+16x^2+64)-16x^2`
`=[(x^2)^2+2.x².8+8²]-16x^2`
`=(x^2+8)^2-(4x)²`
`=(x^2+4x+8)(x^2-4x+8)`
`b)x^4+4y^4`
`=x^4+4x²y²-4x²y²+4y^4`
`=(x^4+4x²y²+4y^4)-4x²y²`
`=[(x^2)^2+2.x².2y²+(2y^2)^2]-4x²y²`
`=(x^2+2y^2)^2-(2xy)^2`
`=(x^2+2xy+2y^2)(x^2-2xy+2y^2)`
`c)x^5+x^4+1`
`=x^5+x^4+x^2-x^2+1`
`=(x^5-x^2)+(x^4+x^2+1)`
`=x^2(x^3-1)+(x^4+2x^2-x^2+1)`
`=x^2(x-1)(x^2+x+1)+[(x^4+2x^2+1)-x^2]`
`=x^2(x-1)(x^2+x+1)+{[(x^2)^2+2.x².1+1²]-x^2}`
`=x^2(x-1)(x^2+x+1)+[(x^2+1)^2-x^2]`
`=x^2(x-1)(x^2+x+1)+(x^2+x+1)(x^2-x+1)`
`=(x^2+x+1)[x^2(x-1)+(x^2-x+1)]`
`=(x^2+x+1)(x^3-x^2+x^2-x+1)`
`=(x^2+x+1)(x^3-x+1)`
`d)x^8+x^4+1`
`=x^8+2x^4-x^4+1`
`=(x^8+2x^4+1)-x^4`
`=[(x^4)^2+2.x^4 .1+1^2]-x^4`
`=(x^4+1)^2-(x^2)^2`
`=(x^4+x^2+1)(x^4-x^2+1)`
`=(x^4+2x^2-x^2+1)(x^4-x^2+1)`
`=[(x^4+2x^2+1)-x^2](x^4-x^2+1)`
`={[(x^2)^2+2.x^2 .1+1^2]-x^2}(x^4-x^2+1)`
`=[(x^2+1)^2-x^2](x^4-x^2+1)`
`=(x^2+x+1)(x^2-x+1)(x^4-x^2+1)`
`e)x^7+x^2+1`
`=x^7+x^2+x-x+1`
`=(x^7-x)+(x^2+x+1)`
`=x(x^6-1)+(x^2+x+1)`
`=x[(x^3)^2-1^2]+(x^2+x+1)`
`=x(x^3+1)(x^3-1)+(x^2+x+1)`
`=x(x^3+1)(x-1)(x^2+x+1)+(x^2+x+1)`
`=(x^2+x+1)[x(x^3+1)(x-1)+1]`
`=(x^2+x+1)[(x^4+x)(x-1)+1]`
`=(x^2+x+1)(x^5-x^4+x^2-x+1)`
`f)x^10+x^5+1`
`=x^10+x^5+x^2-x^2+x-x+1`
`=(x^10-x)+(x^5-x^2)+(x^2+x+1)`
`=x(x^9-1)+x^2(x^3-1)+(x^2+x+1)`
`=x[(x^3)^3-1^3]+x^2(x-1)(x^2+x+1)+(x^2+x+1)`
`=x(x^3-1)(x^6+x^3+1)+x^2(x-1)(x^2+x+1)+(x^2+x+1)`
`=x(x-1)(x^2+x+1)(x^6+x^3+1)+x^2(x-1)(x^2+x+1)+(x^2+x+1)`
`=(x^2+x+1)[x(x-1)(x^6+x^3+1)+x^2(x-1)+1]`
`=(x^2+x+1)[(x^2-x)(x^6+x^3+1)+x^3-x^2+1]`
`=(x^2+x+1)(x^8+x^5+x^2-x^7-x^4-x+x^3-x^2+1)`
`=(x^2+x+1)(x^8-x^7+x^5-x^4+x^3-x+1)`
`g)x³+y³+z³-3xyz`
`=x³+y³+z³-3xyz+3x²y-3x²y+3xy²-3xy²`
`=(x³+3x²y+3xy²+y³)+z³-(3x²y+3xy²+xyz)`
`=(x+y)³+z³-3xy(x+y+z)`
`=(x+y+z)[(x+y)²-z(x+y)+z²]-3xy(x+y+z)`
`=(x+y+z)[(x+y)²-z(x+y)+z²-3xy]`
`=(x+y+z)(x²+2xy+y²-xz-yz+z²-3xy)`
`=(x+y+z)(x²+y²+z²-xy-yz-xz)`
