The other two one-of-a-kind factoring formulas you"ll must memorize are very comparable to one another; they"re the formulas because that factoring the sums and the differences of cubes. Below are the 2 formulas:
You"ll discover in an ext advanced classes just how they come up with these formulas. Because that now, simply memorize them.
You are watching: X^3+8 expanded
To assist with the memorization, first notice that the terms in each of the 2 factorization recipe are precisely the same. Then notification that each formula has only one "minus" sign. The difference between the 2 formulas is in the ar of the one "minus" sign:
For the difference the cubes, the "minus" sign goes in the straight factor, a – b; because that the sum of cubes, the "minus" sign goes in the quadratic factor, a2 – ab + b2.
Some people use the mnemonic "SOAP" to aid keep track of the signs; the letters stand for the linear aspect having the "same" authorize as the authorize in the center of the original expression, then the quadratic factor starting with the "opposite" authorize from what was in the original expression, and also finally the second sign within the quadratic element is "always positive".
Whatever an approach best helps you keep these formulas straight, use it, since you must not assume the you"ll be provided these recipe on the test. You should expect to need to understand them.
See more: What Does Mikasa Mean In English, Mikasa Name Meaning & Origin
Note: The quadratic section of every cube formula does not factor, so don"t waste time attempting to element it. Yes, a2 – 2ab + b2 anda2+ 2ab + b2 factor, yet that"s due to the fact that of the 2"s on their center terms. These sum- and also difference-of-cubes formulas" quadratic state do not have the "2", and thus cannot factor.
When you"re offered a pair of cubes to factor, carefully use the suitable rule. Through "carefully", I typical "using clip to keep track the everything, specifically the an unfavorable signs". Right here are some common problems:element x3 – 8
This is identical to x3 – 23. With the "minus" sign in the middle, this is a distinction of cubes. To execute the factoring, I"ll be plugging x and 2 into the difference-of-cubes formula. Act so, i get: