Adding and Subtracting Polynomials

Adding and Subtracting Polynomials can be thought of as locating all like terms within an expression and combining them. Then writing the answer in Standard Form.
Only like terms can be combined. So remember the two terms must contain the same letter (variable) and it must have the same exponent for both terms in order to be considered like terms.

Polynomial means you have an expression with many terms, with all like terms combined. Polynomials are just expressions, like: 3+5x, -4x-3, 5x2+11x+2. Because polynomials have many terms, to simplify an expression, we must locate and combine all like terms. Then we will write the answer in Standard Form (biggest exponented term to smallest).
Example #1: Add the polynomials: (5x + 2) + (3x + 4)
  1. Remove the parentheses since neither has a number infront of it: 5x + 2 + 3x + 4
  2. Group like terms: 5x + 3x + 2 + 4
  3. Simplify: 8x + 6
Example #2: Add the polynomials: (2x2 + 2x + 6) + (5x + 1)
  1. Remove the parentheses since neither has a number infront of it: 2x2 + 2x + 6 + 5x + 1
  2. Group like terms: 2x2 + 2x + 5x + 6 + 1
  3. Simplify: 2x2 + 7x + 7
Example #3: Subtract the polynomials: (3x2 + 4x + 8) - (2x + 6)
  1. Remove the parentheses since neither has a number infront of it. Also remember if the problem is subtraction, you must subtract all terms in the set of parentheses after the subtract sign: 3x2 + 4x + 8 - 2x - 6
  2. Group like terms: 3x2 + 4x - 2x + 8 - 6
  3. Simplify: 3x2 + 2x + 2
Example #4: Subtract the polynomials: (x2 - 3x + 4) - (2x2 + 5x + 7)
  1. Remove the parentheses since neither has a number infront of it. Also remember if the problem is subtraction, you must subtract all terms in the set of parentheses after the subtract sign: x2 - 3x + 4 - 2x2 - 5x - 7
  2. Group like terms: x2 - 2x2 - 3x - 5x + 4 - 7
  3. Simplify: -x2 - 8x - 3
Example #5: Simplify: 4 + 6m - 8m + 6
  1. Group like terms: 6m - 8m + 4 + 6
  2. Simplify: -2m + 10
Example #6: Simplify: (3x2+ 2x + 5) + (4x2+ 3x + 8)
  1. If there are no numbers infront of either set of parentheses, you can drop all parentheses: 3x2 + 2x + 5 + 4x2 + 3x + 8
  2. Group like terms: 3x2 + 4x2 + 2x + 3x + 5 + 8
  3. Simplify: 7x2 + 5x +13
Example #7: Simplify: (2x2 + 5x + 6) + (x2 - 5x + 6)
  1. If there are no numbers infront of either set of parentheses, you can drop all parentheses: 2x2 + 5x + 6 + x2 - 5x + 6
  2. Group like terms: 2x2 + x2 + 5x - 5x + 6 + 6
  3. Simplify: 3x2 + 12
Example #8: Simplify: (-2x2 - 3x + 5) + (3x2 + 6x - 8)
  1. If there are no numbers infront of either set of parentheses, you can drop all parentheses: -2x2 - 3x + 5 + 3x2 + 6x - 8
  2. Group like terms: -2x2 + 3x2 - 3x + 6x + 5 - 8
  3. Simplify: x2 + 3x - 3
Example #9: Simplify: (5x2 - 2x - 7) - (2x2 + 3x - 4)
  1. If there are no numbers infront of either set of parentheses, you can drop all parentheses: 5x2 - 2x - 7 - 2x2 - 3x + 4
  2. Group like terms: 5x2 - 2x2 - 2x - 3x - 7 + 4
  3. Simplify: 3x2 - 5x - 3
Example #10: Simplify: (4x2 + 6x + 2) - (5x2 - 2x + 7)
  1. If there are no numbers infront of either set of parentheses, you can drop all parentheses: 4x2 + 6x + 2 - 5x2 + 2x - 7
  2. Group like terms: 4x2 - 5x2 + 6x + 2x + 2 - 7
  3. Simplify: -x2 + 8x - 5

Rule: Don't forget that if a number has a subtract sign infront of it, when you take the term out of the context of the expression, you must include the subtract sign infront of the number and then the number acts as a negative number would.