To prove the formula for factoring the difference of two perfect cubes use :
A) a-b square root a²+ab+b²
Step-by-step explanation:
The two special factorizing formula you need to memorize are:
- Factorizing a sum of cubes that follows; a³+b³=(a+b)(a²-ab+b²)
- Factorizing a difference of cubes ; a³-b³=(a-b)(a²+ab+b²)
In these two formula, the terms are the same and each formula has one minus sign.The position of the minus sign brings in the difference in the formulas.
In this case, for difference of cubes; the minus sign occupies the in the linear factor (a-b), where as for the sum of cubes, the minus sign is located in the quadratic factor ;( a²-ab+b²)
For example;
a³-8 = x³-2³
=(x-2)(x²+2x+2²)
=(x-2)(x²+2x+4)
Here you notice that x and 2 are put in the difference of cubes formula
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Keywords : long division, formula, factorize, difference of two perfect cubes
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