when you're adding polynomials , how do you simplify the like terms ?

Question

(12a[to the fourth power]b - (subtract) 7a[to the second power]b[to the second power] + (add) 8ab[to the third power] ) + (-6a[to the fourth power]b - (subtract) 5a[to the second power]b[to the second power] + (add) 3ab[to the third power] )

like when i get the answer for all of these, what do i do next ??? (how do i simplify it)

 

              

Answer 1

Problem: 12a⁴b - 7a²b² + 8ab³ -6a⁴b - 5a²b² + 3ab³

Answer: We want to look at those terms that have the same variable and exponent. They need to match. 

Let's make first put these in order, bunching all the like terms. 

12a⁴b - 6a⁴b + 8ab³ + 3ab³ - 7a²b² - 5a²b²

Do you see how the  colored variables are the same? Because they are the same, we only need to perform the operations on the coefficients. 

Let's add these up. Remember, group like terms.

= (12-6)a⁴b + (8+3)ab³ + (-7-5)a²b²

= 6a⁴b + 11ab³ - 12a²b² 

Final answer. Do you see how we can't go any further? None of the variables are the same, and so we stop here. 

Hope this helps

Stephanie