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

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Answer 1 · 2018-06-24T07:04:39

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

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

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

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

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

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

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