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3 Algebraic Rules Of Expansion

Updated: Jun 16, 2021

(a+b)² = a²+2ab+b²

(a-b)² = a²-2ab+b²

(a+b)(a-b) = a²-b²


The three algebraic rules of expansion are the core of Algebra. We will be using them regularly in all levels of Secondary Math.



Also, the three algebraic rules of expansion are widely tested in O Level and N Level Math Examinations too. Hence, Math Lobby will be teaching you how to apply these 3 algebraic rules today.


Rule 1: (a+b)² = a²+2ab+b²


Question: Expand (2x+4)²


(2x+4)²

= (2x)²+2(2x)(4)+4²

= 4x²+16x+16

- Let 2x be a and 4 be b

- Substitute into Rule 1: (a+b)² = a²+2ab+b²

- Question solved!


Rule 2: (a-b)² = a²-2ab+b²


Question: Expand (3x-2)²

(3x-2)²

= (3x)²-2(3x)(2)+2²

= 9x²-12x+4


Math Lobby Tips:


- Let 3x be a and 2 be b

- Substitute into Rule 2: (a-b)² = a²-2ab+b²

- Question solved!


Rule 3: (a+b)(a-b) = a²-b²


Question: Expand 25x²-16y²

25x²-16y²

= (5x+4)(5x-4)


- Let √25 be a and √16 be b

- Substitute into Rule 3: (a+b)(a-b) = a²-b²

- Question solved!


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