# What is the standard form of  y= (x + 2)(x - 2)(x + y) ?

Jun 2, 2016

$y = {x}^{3} + {x}^{2} y - 4 x - 4 y$

#### Explanation:

First perform the multiplications on the right side.

$y = \left(x + 2\right) \left(x - 2\right) \left(x + y\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left({x}^{2} - 4\right) \left(x + y\right)$

$\textcolor{w h i t e}{\text{XXX}} = {x}^{3} - 4 x + {x}^{2} y - 4 y$

Note the degree of each term:
(the degree of a term is the sum of its variable exponents)
color(white)("XXX"){: (color(black)("term"),,color(black)("degree")), (x^3,,3), (-4x,,1), (+x^2y,,3), (-4y,,1) :}

Arrange the terms in descending degree order with lexicographic preference to terms of the same degree based on their variables.

$y = {x}^{3} + {x}^{2} y - 4 x - 4 y$