query: Completely factoring $a^3 + b^3 + c^3 - 3abc$?
positive_passages.docid: 19940
positive_passages.text: How to show that $A^3+B^3+C^3 - 3ABC = (A+B+C)(A+B\omega+C\omega^2)(A+B\omega^2+C\omega)$ indirectly?
negative_passages.docid: 126385
negative_passages.text: How to prove $a^3 + b^3 +c^3 - 3abc =1 $, If a,b,c are infinite series as given in the description box below?
negative_passages.docid: 23638
negative_passages.text: $a^2b^2+a^2c^2+b^2c^2\leq 3$
negative_passages.docid: 216
negative_passages.text: In a $\triangle ABC,a^2+b^2+c^2=ac+ab\sqrt3$,then the triangle is
negative_passages.docid: 15985
negative_passages.text: simplify $(a_1 + a_2 +a_3+... +a_n)^m$
negative_passages.docid: 102204
negative_passages.text: Factoring product of two primes from solutions of congruence
negative_passages.docid: 138894
negative_passages.text: Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
negative_passages.docid: 44705
negative_passages.text: Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
negative_passages.docid: 67666
negative_passages.text: show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
negative_passages.docid: 29963
negative_passages.text: $6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
negative_passages.docid: 16176
negative_passages.text: Primitive Pythagorean triple divisible by 3
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 105395
negative_passages.text: Minimal polynomial of $1 + 2^{1/3} + 4^{1/3}$
negative_passages.docid: 23080
negative_passages.text: Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
negative_passages.docid: 99692
negative_passages.text: Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
negative_passages.docid: 92518
negative_passages.text: mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
negative_passages.docid: 53725
negative_passages.text: Factor $(x+y)^4+x^4+y^4$