ACT Preparation / Unit 8 ACT 0713 short lesson, about 20 seconds
Sums and Differences of Cubes
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The idea
A sum of cubes factors as a³ + b³ = (a + b)(a² − ab + b²), and a difference of cubes as a³ − b³ = (a − b)(a² + ab + b²).
In practice
x³ − 8 = (x − 2)(x² + 2x + 4).
Where people slip
The binomial factor carries the original sign, and the trinomial's middle term carries the opposite sign.
Your place on the trail
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