Most alzebric formula

 (a+b)²=a²+2ab+b²

(a+b)²=(a-b)²+4ab

(a+b)²=(a+b)(a+b)

(a-b)²=a²-2ab+b²

(a-b)²=(a+b)²-4ab

(a-b)²=(a-b)(a-b)

a²-b²=(a+b)(a-b)

a⁴-b⁴=(a²+b²)(a²-b²)

(a+b+c)²=a²+b²+c²+2ab+2bc+2ca

(a+b-c)²=a²+b²+c²+2ab-2bc-2ca

(a-b-c)²=a²+b²+c²-2ab+2bc-2ca

a²+b²+c²-ab-bc-ca=½[(a-b)²+(b-c)²+(c-a)²]

(a+b)³=a³+b³+3ab(a+b)

(a+b)³=a³+b³+3a²b+3ab²

(a-b)³=a³-b³-3ab(a-b)

(a-b)³=a³-b³-3a²b+3ab²

a³+b³=(a+b)(a²-ab+b²)

a³-b³=(a-b)(a²+ab+b²)

a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)

a³+b³+c³-3abc=½(a+b+c)[(a-b)²+(b-c)²+(c-a)²]

•If a+b+c=0

Then a³+b³+c³-3abc=0

•If a³+b³+c³-3abc=0

Then a+b+c=0

•If a³+b³+c³-3abc=0 and a+b+c≠0

Then a= b=c

• If a³+ b³-c³+3abc=0

Then a+b-c=0

• If a³-b³-c³-3abc=0

Then a-b-c=0