Question

Which of these expressions CANNOT be simplified by combining like terms?

6fg3+4−4f2g2+f3g−12

6fg3+2f(2fg)+4f2g−10

6fg3+5f2g2+f3g−7

6f3g3+7f2g2+4f3g3−10fg

Answer 1

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.

`6fg^3+4-4f^2g^2+f^3 g-12\\\\ 6 f g^3-4 f^2 g^2+f^3 g-8`

2. As, 2 f( 2 f g) and
`4 f^2 g` are like terms, so they can be combined to get
`8 f^2 g`.

`=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`

3.

`=6fg^3+5f^2g^2+f^3g-7`

as,there are no like terms, so, we cannot simplify this expression.→→→Correct Option,This expressions Cannot be simplified by combining like terms

4. As,
`6f^3g^3 and 4f^3g^3` are like terms.They can be combined to get a unique term.

`=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`