`a)`
`(x-2y)(x+2y)+(x+2y)^2`
`=x^2-(2y)^2+x^2+4xy+4y^2`
`=x^2-4y^2+x^2+4xy+4y^2`
`=(x^2+x^2)+(4y^2-4y^2)+4xy`
`=2x^2+4xy`
`b)`
`(x^2-xy+y^2)(x^2+xy+y^2)`
`=(x^2+y^2-xy)(x^2+y^2+xy)`
`=(x^2+y^2)^2-(xy)^2`
`=x^4+2x^2y^2+y^4-x^2y^2`
`=x^4+x^2y^2+y^4`
`c)`
`(x-2y+3z)(x+2y-3z)`
`=[x-(2y-3z)][x+(2y-3z)]`
`=x^2-(2y-3z)^2`
`=x^2-(4y^2-12yz+9z^2)`
`=x^2-4y^2+12yz-9z^2`
`d)`
`(x+2y)^3`
`=x^3+3.x^2 .2y+3.x.(2y)^2+(2y)^3`
`=x^3+6x^2y+12xy^2+8y^3`
`e)`
`(2x^2+3y)^3`
`=(2x^2)^3+3.(2x^2)^2 . 3y+3.2x^2 . (3y)^2 +(3y)^3`
`=8x^6+36x^4y+54x^2y^2+27y^3`
`f)`
`(x-\sqrt{2}y)^3`
`=x^3-3.x^2 . (\sqrt{2}y)+3.x. (\sqrt{2}y)^2-(\sqrt{2}y)^3`
`=x^3-3\sqrt{2}x^2y+6xy^2-2\sqrt{2}y^3`
`g)`
`(1/2x-3)^3`
`=(1/2x)^3-3. (1/2x)^2 . 3+3 . 1/2x . 3^2-3^3`
`=1/8x^3-9/4x^2+27/2x-27`
