Question

Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5? The difference is a binomial with a degree of 5.
The difference is a binomial with a degree of 6.

The difference is a trinomial with a degree of 5.

The difference is a trinomial with a degree of 6.

Answer 1

Let be A =a3b +9a2b2-4ab5, and B=a3b-3a2b2+ab5,so the difference can be defined as A - B =a3b +9a2b2-4ab5 -(a3b-3a2b2+ab5), when there is negative sign in front of the parathesis, all the inside signs must change: that is as follow: A- B= a3b +9a2b2-4ab5 - a3b + 3a2b2 - ab5= a3b-a3b +9a2b2+3a2b2-4ab5- ab5= 12a2b2 -5ab5, the fist term has 2+2=4, as a degree,the second term has 1 +5 =6, so the true answer : The difference is a binomial with a degree of 6

Answer 2

Using the inverse additional property, a3b and a3b cancel out, positive 9a2b2 and 3a2b2 add together to get 12a2b2, and negative -4ab5 and -ab5 add together to -5ab5. Thus. your simplified equation is 12 a2b2 - 5ab5. 

It is a binomial with a degree of 6.