Adding Polynomials
To add polynomials, combine like terms.
Recall that like terms are terms that have the same variables raised to the
same power. That is, like terms have the same variables with the same
exponents.
Like terms
3x, 12x
8xy^{2}, 5.6xy^{2}
24, 11
4xy, 6yx
NOT like terms
7x, 5xy 
The variables do not match.

3x^{2}y^{3}, 2x^{3}y^{2} 
The powers of x do not match.
The powers of y do not match. 
Example 1
Find: (5x^{3}  13x^{2}  7) + (16x^{3} + 8x^{2}
 x + 15)
Solution

(5x^{3}  13x^{2}  7) + (16x^{3} + 8x^{2}
 x + 15) 
Remove the parentheses.

= 5x^{3}  13x^{2}  7 + 16x^{3} + 8x^{2}
 x + 15 
Write like terms next to
each other. 
= 5x^{3} + 16x^{3 } 13x^{2} + 8x^{2 }
 x  7 + 15 
Combine like terms. 
= 21x^{3}  5x^{2}  x + 8 
Note:
We can also place one polynomial beneath
the other and add like terms.
Example 2
Find the sum of (3z^{3} + 2zy^{2}  6y^{3}) and (15z^{3}
 5zy^{2} + 4z^{2}).
Solution
Write the sum.

(3z^{3} + 2zy^{2}  6y^{3}) + (15z^{3}
 5zy^{2} + 4z^{2}) 
Remove the parentheses.

= 3z^{3} + 2zy^{2}  6y^{3} + 15z^{3}
 5zy^{2} + 4z^{2} 
Write like terms next
to each other. 
= 3z^{3} + 15z^{3} + 2zy^{2}
 5zy^{2}  6y^{3} + 4z^{2} 
Combine like terms. 
= 18z^{3}  3zy^{2}  6y^{3} + 4z^{2} 
Note:
We can also place one polynomial beneath
the other and add like terms.
