How to Add Polynomials?

Polynomials can be added similar to simplifying algebraic expressions. That is, group the like terms, solve the groups, and arrange the terms in descending order of exponents, to get the solution.

For example,

Consider the two expressions, (5𝑥𝑦 + 3𝑥³ − 11𝑦² + 2)𝑎𝑛𝑑(7𝑦 − 4𝑥𝑦 + 𝑥³ − 3)to be added.

(5𝑥𝑦 + 3𝑥³ − 11𝑦² + 2) + (7𝑦 − 4𝑥𝑦 + 𝑥³ − 3) = 5𝑥𝑦 + 3𝑥³ − 11𝑦² + 2 + 5𝑥𝑦 + 3𝑥³ − 11𝑦² + 2

= (5𝑥𝑦 − 4𝑥𝑦) + (3𝑥³ + 𝑥³) + (−11𝑦²) + (2 − 3) + 7𝑦

= 𝑥𝑦 + 4𝑥³ − 11𝑦² − 1 + 7𝑦

= 4𝑥³ + 𝑥𝑦 − 11𝑦² + 7𝑦 − 1