1b.+Algebra+-+Teachers

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11. Cubes
math 216x^3 + 8 = (6x)^3 + (2)^3 = (6x + 2)( (6x)^2 - (6x)(2) + (2)^2) math math (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 math math (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 math
 * Encourage students to rewrite expressions as cubes //before// factorising
 * Encourage students to become familiar with the cubes of the first ten integers: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 (these numbers "smell" )
 * Extension option: explore perfect cubes (See Pender 3Unit 1E)
 * Some textbooks, such as Pender, combine cubing binomials with factorising sum/difference of cubes. This may not be a good idea - it confuses the two concepts. Probably better to do cubing binomials immediately after squaring binomials, and save the factorising of sum/difference of cubes to do with the other factorisations.