Question

How do you multiply `[x+(y+1)]^3`?

Answer 1

Remove the internal brackets
`[x+y+1]^3=[x+y+1][x+y+1][x+y+1]`

`[x+y+1][x+y+1]=x^2+xy+x+xy+y^2+y+x+y+1`

`=x^2+y^2+2xy+2x+2y+1`

`[x^2+y^2+2xy+2x+2y+1][x+y+1]=`

`x^3+xy^2+2x^2y+2x^2+2xy+x+x^2y+y^3+2xy^2+2xy+2y^2+y+x^2+y^2+2xy+2x+2y+1`

`x^3+y^3+3x^2y+3xy^2+3x^2+3y^2+6xy+3x+3y+1`