REQUIRED:
To determine which of the given statements cannot be combined.
Step-by-step solution;
To combine like terms when we have terms with unknown values, we look at the variables and their exponential powers. That means x squared and x squared are like terms since the exponential power of both is 2. However, when the exponential powers are different, then they are NOT like terms and therefore cannot be combined. We now have;
[tex]\begin{gathered} x^2\text{ }and\text{ }x^2\text{ }(are\text{ }like\text{ }terms\text{ }and\text{ }can\text{ }be\text{ }combined) \\ \\ x^2\text{ }and\text{ }x^3\text{ }(are\text{ }NOT\text{ }like\text{ }terms\text{ }and\text{ }cannot\text{ }be\text{ }combined) \end{gathered}[/tex]
Therefore, for the expressions given;
[tex]3x^2+5x^2=8x^2[/tex][tex]-10x+8x=-2x[/tex][tex]\begin{gathered} -7x+12x^3 \\ \\ CANNOT\text{ }be\text{ }combined! \end{gathered}[/tex][tex]8x^4-6x^4=2x^4[/tex]
Therefore,
ANSWER:
The third option is the correct answer.
