Adding and Subtracting Polynomials
When adding and subtracting polynomials, you can use the distributive property to add or subtract the coefficients of like terms.
Example:
(2x2 + 5x + 7) + (3x2 –2x + 5)
Use the commutative property to group like terms.
= (2x2 + 3x2) + (5x – 2x) + (7 + 5)
Use the distributive property.
= (2 + 3)x2 + (5 – 2)x + (7 + 5)
= 5x2 + 3x + 12
(Recall that "like terms" are monomials with the same variables, such as 3x2y and 82x2y.)
It may be helpful to arrange the like terms in columns, as with multi-digit addition.
Example:
Subtract.
(x2 + 3xy – 9) – (–2y2 + 5xy + 6)
Arrange vertically.
Subtract term by term.
The solution is x2 + 2y2 – 2xy – 15.
