prepare a chart with all 8 identities
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Identity I: (a + b)2 = a2 + 2ab + b2
Identity II: (a – b)2 = a2 – 2ab + b2
Identity III: a2 – b2= (a + b)(a – b)
Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab
Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)
Identity VII: (a – b)3 = a3 – b3 – 3ab (a – b)
Identity VIII: a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
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⇒ The 8 basic identities are:
- (a + b)²= a² + 2ab + b²
- (a – b)² = a² – 2ab + b²
- a² – b²= (a + b)(a – b)
- (x + a)(x + b) = x² + (a + b) x + ab
- (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
- (a + b)³= a³+ b³+ 3ab (a + b)
- (a – b)³ = a³ – b³ – 3ab (a – b)
- a³ + b³ + c³– 3abc = (a + b + c) (a²+ b²+ c²– ab – bc – ca)
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