Sum and Difference of CubesTwo patterns worth memorising, and the sign rule that keeps…10th GradeBoth a sum and a difference of cubes factor.The signs follow a fixed pattern.a³ ± b³ = (a ± b)(a² ∓ ab + b²)x³ + 8(x+2)(x² − 2x + 4)8 = 2³.x³ − 27(x−3)(x² + 3x + 9)27 = 3³.8x³ + 125(2x+5)(4x² − 10x + 25)8x³ = (2x)³.SignsSame, Opposite, Always PositiveFirst bracket same as the original, then opposite, then plus.THE COMMON MISTAKE✗ x³ + 8 = (x+2)(x+2)(x+2)✓ (x+2)(x² − 2x + 4)Expand the wrong version and the middle terms do not cancel.Unlike squares, a SUM of cubes does factor. That asymmetry catchespeople out.Sum and Difference of Cubeswww.littleactivity.com

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Math · 10th Grade

Sum and Difference of Cubes

Two patterns worth memorising, and the sign rule that keeps them straight.

How to use it

SOAP: Same, Opposite, Always Positive — the three signs in order.

Free · print-ready PDF · US Letter and A4

Grade
10th Grade
Ages
15–16
Subject
Math
Pages
1

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