The other two one-of-a-kind factoring formulas you"ll must memorize are very similar to one another; they"re the formulas for factoring the sums and also the distinctions of cubes. Here are the two formulas:
You"ll discover in an ext advanced classes how they come up v these formulas. Because that now, just memorize them.
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To aid with the memorization, an initial notice the the terms in each of the 2 factorization formulas are exactly the same. Then notification that every formula has only one "minus" sign. The difference between the 2 formulas is in the place of that one "minus" sign:
For the difference of cubes, the "minus" sign goes in the direct factor, a – b; for the sum the cubes, the "minus" sign goes in the quadratic factor, a2 – ab + b2.
Some world use the mnemonic "SOAP" to aid keep track of the signs; the letter stand because that the linear element having the "same" authorize as the sign in the center of the initial expression, then the quadratic factor starting with the "opposite" sign from what remained in the original expression, and also finally the second sign inside the quadratic aspect is "always positive".
Whatever an approach best helps you keep these formulas straight, use it, since you have to not assume the you"ll be given these recipe on the test. You must expect to require to recognize them.
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Note: The quadratic part of every cube formula does not factor, for this reason don"t garbage time attempting to aspect it. Yes, a2 – 2ab + b2 anda2+ 2ab + b2 factor, but that"s due to the fact that of the 2"s ~ above their middle terms. These sum- and also difference-of-cubes formulas" quadratic terms do not have the "2", and also thus cannot factor.
When you"re offered a pair of cubes come factor, carefully use the appropriate rule. By "carefully", I typical "using clip to store track that everything, specifically the negative signs". Here are some typical problems:factor x3 – 8
This is tantamount to x3 – 23. V the "minus" sign in the middle, this is a distinction of cubes. To execute the factoring, I"ll it is in plugging x and 2 right into the difference-of-cubes formula. Law so, ns get: