`a)(x+y)²+(x-y)²`
`=x²+2xy+y²+x²-2xy+y²`
`=2x²+2y²`
`b)2(x+y)(x-y)+(x-y)^2+(x+y)^2`
`=2(x²-y²)+x²+2xy+y²+x²-2xy+y²`
`=2x²-2y²+2x²+2y²`
`=4x²`
`c)2(x+3)^2-3(x+1/2)^2+(x-4)^2`
`=2(x²+6x+9)-3(x²+x+1/4)+x²-8x+16`
`=2x²+12x+18-3x²-3x-3/4+x²-8x+16`
`=x+(133)/4`
`d) 126y^3+(x-5y)(x^2+5xy+25y^2)`
`=126y³+x³-(5y)³`
`=126y³+x³-125y³`
`=x³+y³`