Which of these expressions CANNOT be simplified by combining like terms? 6fg3+4−4f2g2+f3g−126fg3+2f(2fg)+4f2g−106fg3+5f2g2+f3g−76f3g3+7f2g2+4f3g3−10fg

Solution:An expression is said to be like, if there are only constants term in it, otherwise degree of variables in two distinct terms are same.Starting from option (1)1. As, 4 and -12 are like terms, they are combined to get  -8.  [tex]6fg^3+4-4f^2g^2+f^3 g-12\\\\ 6 f g^3-4 f^2 g^2+f^3 g-8[/tex]2. As, 2 f( 2 f g) and [tex]4 f^2 g[/tex] are like terms, so they can be combined to get  [tex]8 f^2 g[/tex].[tex]=6 f g^3+2 f(2 f g)+4 f^2 g-10\\\\ 6 f g^3+4 f^2 g+4 f^2 g-10\\\\ = 6 f g^3+8 f^2 g-10[/tex]3. [tex]=6fg^3+5f^2g^2+f^3g-7[/tex]as,there are no like terms, so, we cannot simplify this expression.→→→Correct Option,This expressions Cannot be simplified by combining like terms4. As, [tex]6f^3g^3 and 4f^3g^3[/tex] are like terms.They can be combined to get a unique term.[tex]=6f^3g^3+7f^2g^2+4f^3 g^3-10 f g\\\\ = 10 f^3 g^3 + 7 f^2 g^2 -10 fg[/tex]