Polynomials can be subtracted 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.
The signs of all the terms of the polynomial that is getting subtracted will be changed. For example,
Consider the expressions, ([latex]3a + 5b – 6 + 19a^{2}b[/latex]) and ([latex]13b^{2}a + 39a^{2}b +17a + 6[/latex]).
The first expression is to be subtracted from the second. That is,
( 13𝑏2𝑎 + 39𝑎2𝑏 + 17𝑎 + 6 ) – (3𝑎 + 5𝑏 − 6 + 19𝑎2𝑏 ) = 13𝑏2𝑎 + 39𝑎2𝑏 + 17𝑎 + 6 − 3𝑎 − 5𝑏 + 6 − 19𝑎2𝑏
= 13𝑏2𝑎 + (39𝑎2𝑏 − 19𝑎2𝑏) + (17𝑎 − 3𝑎) + (6 + 6) + (−5𝑏)
= 13𝑏2𝑎 + 20𝑎2𝑏 + 14𝑎 + 12 − 5𝑏
= 20𝑎2𝑏 + 13𝑏2𝑎 + 14𝑎 − 5𝑏 + 12