Math Tutoring on Factoring a Sum or Difference of Cubes
The sum or difference of two cubes can be factored into a product of binomial times a trinomial. That is, x³+y³=(x+y)(x²−xy+y²) and x³−y³=(x−y)(x²+xy+y²). A mnemonic for the signs of the factorization is the word "SOAP", the letters stand for "Same sign" as in the middle of the original expression, "Opposite sign", and "Always Positive".
That is x³±y³=(x[Same sign]y)(x²[Opposite sign]xy[Always Positive]y²)
Here are the steps required for factoring a sum of cubes which is followed in math tutoring:
Step 1: Decide if the two terms have anything in common, called the greatest common factor or GCF. If so, factor out the GCF. Do not forget to include the GCF as part of your final answer.
Step 2: Rewrite the original problem as a difference of two perfect cubes.
Step 3: Use the following sayings to help write the answer: “Write What You See”, “Square-Multiply-Square” “Same, Different, End on a Positive”
Step 4: Use these three pieces to write the final answer.
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1. What is factoring the sum and difference of two cubes?
2. How do you factor perfect cubes?
3. How do you factor a cubic binomial?
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