Question

How do you simplify `3y ^ { 2} + 2x y + 1+ 3x + y + 2x ^ { 2}`?

Answer 1

It cannot be simplified further,

Explanation:

The . expression cannot be simplified, There are six terms but they cannot be added because they are all different (unlike).

Only like terms which have exactly the same variables and powers can be added or subtracted.

Answer 2

This is already in simplest form and does not factor either.

Explanation:

Given:

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

This is in simplest form in that none of the terms can be combined, but it is interesting to ask whether it can be factored.

Ignoring all of the terms involving `y`, we have:

`1+3x+2x^2 = (2x+1)(x+1)`

Ignoring all of the terms involving `x`, we have:

`3y^2+y+1`

This has discriminant `Delta = 1^2-4(3)(1) = -11 < 0`, so does not factor using real coefficients.

We can deduce that the original polynomial does not factor using real coefficients, since otherwise putting `x=0` would yield a factorisation of `3y^2+y+1`.