## Summary

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**Algebraic identities of second degree**

- (a + b)
^{2}= a^{2}+ 2ab + b^{2} - (a – b)
^{2}= a^{2}– 2ab + b^{2} - a
^{2}– b^{2}= (a + b)(a – b) - (x + a)(x + b) = x
^{2}+ (a + b)x + ab - (a + b + c)
^{2}= a^{2}+ b^{2}+ c^{2}+ 2ab + 2bc + 2ca

These identities can be used to factorise quadratic polynomials. A polynomial is said to be cubic polynomial if its degree is three. Cubic polynomials can be factorised using factor theorem. The algebraic identities used in factorising a third degree polynomial are:

- (a + b)
^{3}= a^{3}+ b^{3}+ 3ab (a + b) - (a – b)
^{3}= a^{3}– b^{3}– 3ab (a – b) - a
^{3}+ b^{3}= (a + b)(a^{2}– ab + b^{2}) - a
^{3}– b^{3}= (a – b)(a^{2}+ ab + b^{2}) - a
^{3}+ b^{3}+ c^{3 }– 3abc = (a + b + c)(a^{2}+ b^{2}+ c^{2}– ab – bc – ca)