⚠️Here's a list of some of the most frequently used algebraic identities:

* Square of a Binomial (Difference):
(a-b)^2 = a^2 - 2ab + b^2
Example: (x-3)^2 = x^2 - 2(x)(3) + 3^2 = x^2 - 6x + 9

* Difference of Squares:
a^2 - b^2 = (a-b)(a+b)
Example: x^2 - 25 = x^2 - 5^2 = (x-5)(x+5)

* Sum of Cubes:
a^3 + b^3 = (a+b)(a^2 - ab + b^2)
Example: x^3 + 8 = x^3 + 2^3 = (x+2)(x^2 - 2x + 4)

* Difference of Cubes:
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
Example: y^3 - 27 = y^3 - 3^3 = (y-3)(y^2 + 3y + 9)

* Cube of a Binomial (Sum):
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
Example: (x+1)^3 = x^3 + 3(x^2)(1) + 3(x)(1^2) + 1^3 = x^3 + 3x^2 + 3x + 1

* Cube of a Binomial (Difference):
(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
Example: (2x-y)^3 = (2x)^3 - 3(2x)^2(y) + 3(2x)(y^2) - y^3 = 8x^3 - 12x^2y + 6xy^2 - y^3

* Square of a Trinomial:
(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
Example: (x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx

* Sum of Cubes (Special Case):
If a+b+c=0, then a^3+b^3+c^3 = 3abc.

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