Adding & Subtracting Polynomials
Adding and subtracting polynomials comes down to combining like terms — terms that share the same variable and exponent. Only like terms combine.
Subtraction has one trap: distribute the negative to every term in the second polynomial before combining. Handle that and the rest is arithmetic.
Combine like terms
Line up terms with the same power of and add their coefficients. An term only combines with another term.
Unlike terms — different powers — just carry along unchanged into the answer, written in standard form.
Distribute the subtraction
When subtracting, the minus sign applies to every term in the second polynomial, flipping each sign. Rewrite the subtraction as adding the opposite first.
This is where most errors happen — a missed sign on an inner term. Distribute carefully, then combine like terms.
Worked examples
Example 1: adding
Add .
Answer:
Example 2: subtracting
Subtract .
Answer:
Try one yourself
Common questions
What are like terms?
Terms with the identical variable and exponent, such as and . Only like terms can be combined.
What is the biggest mistake when subtracting?
Forgetting to distribute the minus sign to every term in the second polynomial. Rewrite subtraction as adding the opposite to avoid it.
Should the answer be in standard form?
Yes — order the combined terms from highest degree to lowest.
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