`a)``x^8+64`
`=x^8+16x^4-16x^4+64`
`=(x^8+16x^4+64)-16x^4`
`=[(x^4)^2+2.8.x^4+8^2]-(4x^2)^2`
`=(x^4+8)^2-(4x^2)^2`
`=(x^4+8-4x^2)(x^4+8+4x^2)`
`b)x^4+4y^2`
`=x^4+4x^2y^2-4x^2y^2+4y^2`
`=(x^4+4x^2y^2+4y^2)-4x^2y^2`
`=[(x^2)^2+2.x^2. 2y^2+(2y^2)^2]-(2xy)^2`
`=(x^2+2y^2)^2-(2xy)^2`
`=(x^2+2y^2+2xy)(x^2+2y^2-2xy)`