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The other two one-of-a-kind factoring recipe you"ll must memorize space very similar to one another; they"re the formulas for factoring the sums and also the differences of cubes. Below are the two formulas:


You"ll find out in more advanced classes just how they come up with these formulas. Because that now, simply memorize them.

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To assist with the memorization, very first notice the the terms in each of the 2 factorization recipe are specifically the same. Then notice that every formula has only one "minus" sign. The distinction between the two formulas is in the location of the one "minus" sign:

For the difference the cubes, the "minus" authorize goes in the linear factor, ab; 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 for the linear factor having the "same" authorize as the sign in the center of the original expression, climate the quadratic factor beginning with the "opposite" authorize from what remained in the original expression, and finally the 2nd sign inside the quadratic factor is "always positive".


Whatever method best help you store these recipe straight, usage it, due to the fact that you need to not assume the you"ll be offered these formulas on the test. You have to 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 rubbish time attempting to element it. Yes, a2 – 2ab + b2 anda2+ 2ab + b2 factor, however that"s due to the fact that of the 2"s on their center terms. This sum- and also difference-of-cubes formulas" quadratic terms do not have the "2", and thus cannot factor.

When you"re given a pair that cubes to factor, carefully use the appropriate rule. By "carefully", I average "using parentheses to keep track that everything, especially the an unfavorable signs". Right here are some common problems:

variable x3 – 8

This is indistinguishable to x3 – 23. V the "minus" sign in the middle, this is a distinction of cubes. To execute the factoring, I"ll be plugging x and 2 right into the difference-of-cubes formula. Doing so, i get: