\(( a\pm b)^2=a^2 \pm2ab + b^2\)
\(( a\pm b)^3=a^3\pm3a^2b+3ab^2 + b^3\)
\(( a\pm b)^4=a^4\pm4a^3b+6a^2b^2\pm4ab^3+ b^4\)
\((a + b+ c)^2=a^2+b^2+c^2+2ab+2ac+2bc\)
\((a + b-c)^2=a^2+b^2+c^2+2ab-2ac-2bc\)
\((a - b-c)^2=a^2+b^2+c^2-2ab-2ac+2bc\)
\((a + b+c)^3=a^3+b^3+c^3+6abc+3(a^2b+ab^2+b^2c+bc^2+c^2a+ca^2)\)
\((a_1 + a_2+...+ a_n)^2=a_1^2+a_2^2+....+a_n^2+2(a_1a_2+a_1a_3+....+a_{n-1}a_n)\)
\(a^2-b^2= (a-b)(a+b)\)
\(a^3+b^3= (a+b)(a^2 -ab+b^2)\)
\(a^3-b^3= (a-b)(a^2 +ab+b^2)\)
\(a^4+b^4= (a^2+b^2)^2-2a^2b^2\)
\(=(a^2 +\sqrt{2}ab+b^2)(a^2 -\sqrt{2}ab+b^2)\)
\((a^4-b^4)=(a^2-b^2)(a^2+b^2)\)
\(=(a+b)(a-b)(a^2+b^2)\)
\(a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)\)
\(a^5-b^5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)\)
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