The Sum and Difference of Cubes
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State
The sum of cubes factors as a³ + b³ = (a + b)(a² − ab + b²); the difference mirrors it with the signs flipped.
Show
x³ + 8 = (x + 2)(x² − 2x + 4); multiplying back, the middle products cancel in pairs.
Watch for
The trinomial's middle sign opposes the binomial's.
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- Nothing yet depends on this.