Important Algebraic Formulas
(a+b)²= a² + b² + 2ab
(ab)²= a² + b²-2ab
a²-b²= (a+b)(a-b)
a²+b²= (a+b)²-2ab or a²+b²= (ab)²+2ab
a³+b³ = (a + b)(a²-ab+b²) = (a+b)³-3ab(a+b)
a³-b³ = (a - b)(a²+ab+b²) = (ab)³+3ab(a - b)
2(a²+b²) = (a+b)²+ (ab)²
(a+b)²(ab)² = 4ab
a³+b³ = (a + b)(ab)[(a+b)²-2ab]
(ab)²= (a+b)² - 4ab
(a+b)²= (ab)² + 4ab
a² + b² = [(a+b)²-2ab]2-2(ab)²
(a+b+c)² = a²+b²+c²+2ab+2bc + 2ca
(a+bc)² = a²+b²+c² + 2ab - 2bc-2ca
(a-b-c)²= a²+b²+c²-2ab + 2bc-2ca
a³+b³+c³-3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)
a² + a²b²+b²= (a²+ab+b²) (a² - ab + b²
a² + a² + 1 = (a²+a+1)(a²-a+1)
if a+b+c=0 then a³+b³+c³ = 3abc
a³-b³ = (a+b)(a²+b²)(a+b)(a-b)
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