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Math formulas: Factoring and product formulas

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Factoring Formulas

Factoring and product formulas
a2b2=(ab)(a+b)a^2 - b^2 = (a-b)(a+b)
a3b3=(ab)(a2+ab+b2)a^3 - b^3 = (a-b)\left(a^2 + ab + b^2\right)
a3+b3=(a+b)(a2ab+b2) a^3 + b^3 = (a+b)\left(a^2 - ab + b^2\right)
a4b4=(ab)(a+b)(a2+b2) a^4 - b^4 = (a-b)(a+b)\left(a^2 + b^2\right)
a5b5=(ab)(a4+a3b+a2b2+ab3+b4) a^5 - b^5 = (a-b)\left(a^4 + a^3b + a^2b^2 + ab^3 + b^4\right)

Product Formulas

(a+b)2=a2+2ab+b2 (a + b)^2 = a^2 + 2ab + b^2
(ab)2=a22ab+b2 (a - b)^2 = a^2 - 2ab + b^2
(a+b)3=a3+3a2b+3ab2+b3 (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
(ab)3=a33a2b+3ab2b3 (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
(a+b)4=a4+4a3b+6a2b2+4ab3+b4 (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
(ab)4=a44a3b+6a2b24ab3+b4 (a - b)^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4
(a+b+c)2=a2+b2+c2+2ab+2ac+2bc (a + b + c)^2 = a^2 + b^2 + c^2 +2ab + 2ac + 2bc
(a+b+c+...)2=a2+b2+c2+...+2(ab+ac+bc+...) (a + b + c + ...)^2 = a^2 + b^2 + c^2 + ... + 2(ab + ac + bc + ... )

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