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How Do You Subtract Polynomials?

Find the difference between these two polynomials: (6a3+12a2-15a) and (4a2-12a+8)

Summary

  1. 'a' is a variable
  2. These are two polynomials
  3. The word 'difference' means that we are subtracting
  4. Distribute the negative sign into the parentheses
  5. Distributing the negative sign flips the signs of the terms inside the parentheses
  6. Identify like terms and group them together
  7. 12a2 and -4a2 are like terms
  8. -15a and 12a are like terms

Notes

    1. The two sets of parentheses contain polynomials
    1. This is the resulting equation after distributing in the '-' sign
    2. 'a' is a variable
    3. The left set of parentheses just disappears
    4. All the numbers that were in the second set of parentheses have their signs flipped
    1. The first set of parentheses was not behind a negative sign, so the signs inside stayed the same
    2. The second set of parentheses WAS behind a negative sign, so the signs inside flipped
    1. Find terms that contain 'a' to the same power
    1. There are no other terms with an 'a' to the 3rd power
    2. 'a' is a variable
    1. These are the like terms with 'a' to the 2nd power
    2. 'a' is a variable
    1. These are the like terms with 'a' to the 1st power
    2. 'a' is a variable
    1. There are no other terms with an 'a' to the 0 power
    2. 'a' is a variable
    1. Once we group the like terms together, we will be able to add them more easily
    2. We are allowed to move the terms around because of the associative property of addition
    1. 'a' is a variable
    2. Group together the a2 like terms, 12a2 and - 4a2
    3. Then group together the a1 like terms, 12a and -15a
    1. 'a' is a variable
    2. 12a2 - 4a2 = 8a2
    3. 12a - 15a = -3a