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The other two distinct factoring formulas you"ll should memorize are very comparable to one another; they"re the formulas because that factoring the sums and also the differences of cubes. Below are the two formulas:


You"ll discover in an ext advanced classes exactly how they came up with these formulas. For now, just memorize them.

You are watching: (a+b)(a^2-ab+b^2)


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To help with the memorization, very first notice that the terms in each of the two factorization formulas are exactly the same. Then an alert that each formula has only one "minus" sign. The difference between the two formulas is in the ar of the one "minus" sign:

For the difference of cubes, the "minus" sign goes in the straight factor, ab; for the sum of cubes, the "minus" sign goes in the quadratic factor, a2 – ab + b2.


Some world use the mnemonic "SOAP" to assist keep monitor of the signs; the letters stand because that the linear aspect having the "same" sign as the sign in the center of the initial expression, then the quadratic factor beginning with the "opposite" authorize from what was in the initial expression, and also finally the second sign inside the quadratic factor is "always positive".


Whatever technique best helps you keep these formulas straight, use it, since you should not assume the you"ll be offered these recipe on the test. You need to expect to require to understand them.

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Note: The quadratic section of every cube formula does no factor, so don"t rubbish time attempting to factor it. Yes, a2 – 2ab + b2 anda2+ 2ab + b2 factor, but that"s because of the 2"s ~ above their middle terms. These sum- and also difference-of-cubes formulas" quadratic state do no have that "2", and also thus cannot factor.

When you"re given a pair of cubes to factor, carefully apply the suitable rule. By "carefully", I median "using clip to store track that everything, especially the negative signs". Right here are some common problems:

variable x3 – 8

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