Subtracting Polynomials – Examples
You should study problems on subtracting polynomials with examples for your algebra test.
To see the examples, please go to the sections below the following quiz.
Subtracting Polynomials – Quiz
Instructions: Subtract the polynomials in the quiz below after studying the examples in the next section. You will see the answers after each question.
[WpProQuiz 31]
Polynomials with Negatives
When you see a problem about subtracting polynomials, you need to be especially careful with polynomial expressions that contain negative numbers.
You should also view our post on adding polynomials if you need practice with this skill.
Grouping Like Terms
If you see a problem on subtracting polynomials, you need to be sure to group like terms together.
Click here to learn how to group like terms.
The steps for subtracting polynomials are similar to those for adding polynomials because you have to group like terms.
Subtracting Polynomials - Example
When subtracting polynomials you also need to remember that two negative signs together make a positive.
So, when you have to subtract a negative number you actually need to add that number, as shown in step 2 below.
Now study the steps in the following example problem.
Instructions: Subtract the following polynomials.
(2x2 + 3xy + 5y2) – (4x2 – 4xy – 6y2) = ?
Answer: –2x2 + 7xy + 11y2
STEP 1:
Remove the parentheses, paying attention to any negatives.
(2x2 + 3xy + 5y2) – (4x2 – 4xy – 6y2) =
2x2 + 3xy + 5y2 – 4x2 – –4xy – –6y2
STEP 2:
Change subtraction to addition when a negative number is subtracted.
2x2 + 3xy + 5y2 – 4x2 – –4xy – –6y2 =
2x2 + 3xy + 5y2 – 4x2 + 4xy + 6y2
STEP 3:
Group the like terms together using sets of parentheses.
2x2 + 3xy + 5y2 – 4x2 + 4xy + 6y2 =
2x2 – 4x2 + 3xy + 5y2 – 4x2 + 4xy + 6y2 =
2x2 – 4x2 + 3xy + 5y2 + 4xy + 6y2 =
2x2 – 4x2 + 3xy + 4xy + 5y2 + 4xy + 6y2 =
2x2 – 4x2 + 3xy + 4xy + 5y2 + 6y2
STEP 4:
Perform the operations on the terms inside each set of parentheses to solve the problem.
2x2 – 4x2 + 3xy + 4xy + 5y2 + 6y2 =
(2x2 – 4x2) + (3xy + 4xy) + (5y2 + 6y2) =
–2x2 + 7xy + 11y2
Polynomials - Further Practice
If you thought these problems on subtracting polynomials were helpful, you may also want to look at the following posts on polynomials:
