Sum of two cubes
In mathematics, the sum of two cubes is a cubed number added to another cubed number. Factorization Every sum of cubes may be factored according to the identity in elementary algebra. Binomial numbers are the general of this factorization to higher odd powers. "SOAP" method The mnemonic "SOAP", standing for "Same, Opposite, Always Positive", is sometimes used to memorize the correct placement of the addition and subtraction symbols while factorizing cubes. When applying this method to the factorization, "Same" represents the first term with the same sign as the original expression, "Opposite" represents the second term with the opposite sign as the original expression, and "Always Positive" represents the third term and is always positive. {| cellspacing="4" |- style="vertical-align:bottom;text-align:center;line-height:0.9;font-size:90%;" | || originalsign || || Same || || Opposite || || AlwaysPositive |- | || style="border:1px solid;border-bottom:none;"| | || style="border:1px solid;border-bottom:none;"| | || style="border:1px solid;border-bottom:none;"| | || style="border:1px solid;border-bottom:none;"| |- | ! | ! | ! | ! | |- | ! | ! | ! | ! | |} Proof Starting with the expression, is multiplied by a and b By distributing a and b to , one get and by canceling the alike terms, one get Similarly for the