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MATHMAA

# Algebraic Formula

## Probability Introduction :

Basic Algebraic Formula are listed below :

• $$(a+b)^{2} =a^{2}+2ab+b^{2}$$
• $$(a-b)^{2} =a^{2} - 2ab + b^{2}$$
• $$(a+b)^{2} + (a-b)^{2} =2a^{2} + 2b^{2}$$
• $$(a+b)^{2} -(a-b)^{2} = 4ab$$
• $$a^{2} + b^{2} =(a+b)^{2} - 2ab$$
• $$a^{2} + b^{2} = (a-b)^{2} + 2ab$$
• $$a^{2} - b^{2} = (a-b)(a+b)$$
• $$(a+b+c)^{2} = a^{2} + b^{2} + c^{2} + 2ab + 2bc +2ca$$
• $$(a-b+c)^{2} = a^{2} + b^{2} + c^{2} -2ab -2bc + 2ac$$
• $$(a + b -c)^{2} = a^{2} + b^{2} + c^{2} + 2ab -2bc -2ac$$
• $$(a+b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}$$
• $$(a+b)^{3} = a^{3} + b^{3} + 3ab(a+b)$$
• $$(a-b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}$$
• $$(a-b)^{3} = a^{3} - b^{3} -3ab(a-b)$$
• $$a^{3} + b^{3} = (a+b)(a^{2} -ab +b^{2}$$
• $$a^{3} + b^{3} = (a+b)^{3} - 3ab(a+b)$$
• $$a^{3} - b^{3} = (a-b)(a^{2} + ab + b^{2})$$
• $$a^{3} - b^{3} = (a - b)^{3} + 3ab(a-b)$$
• $$(a + b + c)(a^{2} + b^{2} + c^{2} -ab - bc - ca ) = a^{3} + b^{3} + c^{3} -3abc$$
• If a + b + c = 0 then $$a^{3} + b^{3} + c^{3} = 3abc$$
• $$a^{2} + b^{2 } + c^{2} - ab - bc - ca = \frac{1}{2} [(a-b)^{2} + (b-c)^{2} + (c-a)^{2}]$$
• In Algebraic formula we have multiplication of binomials using FOIL METHOD: Which is as follows,
• FOIL METHOD :
F= First terms
O = Outer terms
I = Inner terms
L = Last terms
(a + b ) ( c + d) = ac + ad + bc + bd
• (x+a)(x+b)=$$x^{2}$$+(a+b)x+ab
• $$(a + b)^{4} = a^{4} + 4a^{3}b+ 6a^{2}b^{2} + 4ab^{3} + b^{4}$$
• $$(a- b)^{4} = a^{4} - 4a^{3}b + 6a^{2}b^{2} - 4ab^{3} + b^{4}$$

These are some of Algebraic Formula given.