a To add variables they have to be like terms. Consider the given expression.
4xy^3+5x^3y
Notice the location of the exponent in each term. For the first term, the y factor is being raised, but in the second term the x factor is being raised.
4x y^3+5 x^3y
Therefore, the terms are not like and we cannot add them. This means that our expression is already fully simplified.
b Observing the given expression, we can see that there is a term outside the parentheses that can be distributed.
The given expression was not simplified, because there was a term that could be distributed. The fully simplified expression in this case should be - y+1.
c Let's look at the given expression to see if there are any like terms that could be added.
5x^2+12xy-3yxThe first term has an x^2 and the second has an x0,y so these cannot be added together. However, xy and yx can be added together thanks to the Commutative Property of Multiplication.
