Write down different identities of algebraic expression.

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Solution

Algebric Identities
If and equality holds true for all values of he variable, then it is called an Iidentity.
Iidentity 1: $(x + y)^{2} = x^{2} + 2 x y + y^{2}$
Iidentity 2: $(x - y)^{2} = x^{2} - 2 x y + y^{2}$
Iidentity 3: $(x + y) (x - y) = x^{2} - y^{2}$
Iidentity 4: $(x + y + z)^{2} =^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x$
Iidentity 5: $(x + y)^{3} = x^{3} + y^{3} + 3 x y (x + y)$
Iidentity 6: $(x - y)^{3} = x^{3} - y^{3} - 3 x y (x - y)$
Iidentity 7: $x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$
Iidentity 8: $x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$
Iidentity 9: $x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x) = \frac{1}{2} (x + y + z) {(x - y)^{2} + (y - z)^{2} + (z - x)^{2}}$

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