h⁴+2h²k+k² using algebraic identities
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For example, the identity(x+y)^2 = x^2 + 2xy + y^2(x+y)2=x2+2xy+y2holds for all values of xx and yy.
Since an identity holds for all values of its variables, it is possible to substitute instances of one side of the equality with the other side of the equality. For example, because of the identity above, we can replace any instance of (x+y)^2(x+y)2 with x^2 + 2xy + y^2x2+2xy+y2 and vice versa.
Clever use of identities offers shortcuts to many problems by making the algebra easier to manipulate. Below are lists of some common algebraic identities.