The 5 Rules of Algebraic Expansion and Factorisation

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Easy rules to identify the type of expansion/factorisation
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Rule 1 a (b + c) = ab + ac Example: 2 (x + 3) = 2x + 6
Rule 2 (a+b) (c+d) = ac + ad + bc + bd Example: (r+s) (t+u) = rt + ru + st + su
Rule 3 (a+b) (a+b) = a² + 2ab + b² Example: (x+3) (x+3) = x² + 2 (x) (3) + 3² = x² + 6x + 9
Rule 4 (a-b) (a-b) = a² - 2ab + b² Example: (x-3) (x-3) = x² - 2 (x) (3) + 3² = x² - 6x + 9
Rule 5 (a+b) (a-b) = a² - b² Example: (x+3) (x-3) = x² - 3x + 3x - 3² = x² - 3² = x² - 9
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