Mr. Integral
Math notes/Pre-Calculus/Factoring

Perfect Cubes — Cheat sheet

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Key method

(A+B)3=A3+3A2B+3AB2+B3.(A+B)^3=A^3+3A^2B+3AB^2+B^3. (A−B)3=A3−3A2B+3AB2−B3.(A-B)^3=A^3-3A^2B+3AB^2-B^3.

For subtraction, the signs alternate because odd powers of −B-B are negative.

Example

For 8x3−36x2+54x−278x^3-36x^2+54x-27, try A=2xA=2x, B=3B=3. The mixed terms are −3(2x)2(3)=−36x2-3(2x)^2(3)=-36x^2 and 3(2x)(32)=54x3(2x)(3^2)=54x. Thus the expression is (2x−3)3(2x-3)^3.

Avoid this mistake

A repeated cubic factor crosses the axis at its zero; it does not behave like a repeated square. Multiplicity matters.