Question

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

Answer 1

`y=x^3+x^2y-4x-4y`

Explanation:

First perform the multiplications on the right side.

`y=(x+2)(x-2)(x+y)`

`color(white)("XXX")=(x^2-4)(x+y)`

`color(white)("XXX")=x^3-4x+x^2y-4y`

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^2y-4x-4y`