5a2-6ab+3b2

The terms are $5a^2$, $-6ab$, and $3b^2$.

Like terms have the exact same variables raised to the same powers.

• $5a^2$ has $a^2$.
• $-6ab$ has $ab$.
• $3b^2$ has $b^2$. Since the variable parts ($a^2$, $ab$, $b^2$) are all different, these are unlike terms.

Because there are no like terms, the expression cannot be simplified by combining terms.
To check for factorization into real linear factors, we can consider the discriminant of the quadratic form. For $Ax^2 + Bxy + Cy^2$, the discriminant is $B^2 - 4AC$.
Here, $A=5$, $B=-6$, $C=3$.
The discriminant is $(-6)^2 - 4(5)(3) = 36 - 60 = -24$.
Since the discriminant is negative, this quadratic expression cannot be factored into linear terms with real coefficients.

Therefore, the expression is already in its simplest form.