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Polynomial Addition and Subtraction

HSA-APR.A.1
Answer Keys Here

Aligned To Common Core Standard:

High School - HSA-APR.A.1

How to Add and Subtract Polynomials? By now, you have an understanding of exponents and variables. In fact, you must be familiar with monomials as the singular terms having variables and coefficients If we write these monomials together with a plus or minus sign, we get a polynomial. It is that simple. The sum or difference of monomials is termed as a polynomial. A polynomial usually looks like this: 3 x 2 + 4y + z The above expression is the sum of three monomials; 3 x 2, 4y, and z Similar to monomials, the addition and subtraction of polynomial also follow the rule of like terms. That is, the coefficients with the same variables are added or subtracted but the variables and exponents stay the same. Adding polynomials - Let's explore how the like terms work with polynomials. Let's take one expression to be 3 x 2+ 4y + z and 2 x2 + 5y + 2z as the second expression, and add them. (3 x 2 + 4y + z) + (2 x 2 + 5y + 2z) Remove the parentheses and write like terms together 3 x 2 + 2x2 + 4y + 5y + z + 2z 5 x 2 + 9y + 3z Note how the coefficients have added up while the variable and exponents remain the same Subtracting polynomials - Similar to addition, subtraction also follows the rule of like terms. However, you need to pay close attention to the change of signs Let's take 3x + 4y + 2z and 2x + 3y + z, as two expressions: (3x + 4y + 2z) – (2x + 3y + z) Remove the parentheses and change the signs of subtrahend polynomial: 3x + 4y + 2z – 2x - 3y - z Write the like terms together with their changed signs: 3x - 2x + 4y - 3y + 2z - z Remember to write the sign of greater coefficient with your answer: x + y + z

Printable Worksheets And Lessons






Homework Sheets

The second sheet is done visually. Students will pick up on it quickly.

  • Homework 1 - We cannot combine 5a^2 and 9a because they are not like terms.
  • Homework 2 - These algebra boxes represent the addition problem. We have use the algebra tiles to solve the addition problems.
  • Homework 3 - Like terms are terms that have the same variables raised to the same powers.



Practice Worksheets

The blocks are the middle sheet as well here.

  • Practice 1 - We have to add like terms and their coefficients.
  • Practice 2 - Use algebra tiles to add (1k + 6) + (3k + 2).
  • Practice 3 - Find the final value of the following problems.



Math Skill Quizzes

I like to have the kids get of the habit of thinking of each polynomial as three separate parts.

  • Quiz 1 - (3z^2 + 5z + 3) + (4z + 4)
  • Quiz 2 - Use algebra tiles to add (3y + 3) + (2y + 2)
  • Quiz 3 - Place all of these things together to get a final review in.