Call a spade... something else

a)  5x + 3
+  2x + 6   =      ??????

b) 3x²  +  4x

+ 4x²  +  5x =      ??????

Some of my past students seemed to want to add the "x's" together, getting answers such as...

a)  5x + 3
+  2x + 6   =          7x² + 9        or....

b) 3x² + 4x

+ 4x² + 5x =              7x⁴ + 9 x²

My advice, always, is not to call a spade "a spade", but to use the good old cat and dog to help us. (Or any other animal you might choose.) For question a)...

Restate the question as 5 cats and 3 dogs ADDED to 2 more cats and 6 more dogs. You'll get 7 cats and 9 dogs. None of those cats gets squared or changed to a super cat, nuclear powered cat, robo-cat or anything else.  So your answer is...

7x + 9 

For question b) ... you'll simply have 3 elephants and 4 cats ADDED to 4 elephants and 5 cats. Your answer is...

7x² + 9 x

It is easy to get blinded by all the exponents when you get questions such as...

 7x² + 2y + 9x⁴  +  8x² + 3y + 3x⁴ 

It is much easier to imagine 15 elephants, 5 giraffes and 12 monkeys.