**Important Basic Formulas in Equations**:

**(a + b)(a – b) = a**^{2}– b^{2}**(a + b + c)**^{2}= a^{2}+ b^{2}+ c^{2}+ 2(ab + bc + ca)**(a ± b)**^{2}= a^{2}+ b^{2}± 2ab**(a + b + c + d)**^{2}= a^{2}+ b^{2}+ c^{2}+ d^{2}+ 2(ab + ac + ad + bc + bd + cd)**(a ± b)**^{3}= a^{3}± b^{3}± 3ab(a ± b)-
**(a ± b)(a**^{2}+ b^{2}m ab) = a^{3}± b^{3} **(a + b + c)(a**^{2}+ b^{2}+ c^{2}-ab – bc – ca) = a^{3}+ b^{3}+ c^{3}– 3abc =**1/2 (a + b + c)[(a - b)**^{2}+ (b - c)^{2}+ (c - a)^{2}]**when a + b + c = 0, a**^{3}+ b^{3}+ c^{3}= 3abc**(x + a)(x + b) (x + c) = x**^{3}+ (a + b + c) x^{2}+ (ab + bc + ac)x + abc**(x – a)(x – b) (x – c) = x**^{3}– (a + b + c) x^{2}+ (ab + bc + ac)x – abc**a**^{4}+ a^{2}b^{2}+ b^{4}= (a^{2}+ ab + b^{2})( a^{2}– ab + b^{2})**a**^{4}+ b^{4}= (a^{2}– √2ab + b^{2})( a^{2}+ √2ab + b^{2})**a**^{n}+ b^{n}= (a + b) (a^{n-1}– a^{n-2}b + a^{n-3}b^{2}– a^{n-4}b^{3}+…….. + b^{n-1})(valid only if n is odd)**a**^{n}– b^{n}= (a – b) (a^{n-1}+ a^{n-2}b + a^{n-3}b^{2}+ a^{n-4}b^{3}+……… + b^{n-1}){were n**ϵ****N****)****(a ± b)**^{2n}is always positive while -(a ± b)^{2n}is always negative, for**any****real values of****a and b****(a – b)**^{2n}= (b – a)^{2}” and (a – b)^{2n+1}= – (b – a)^{2n+1}**if α and β are the roots of equation ax**^{2}+ bx + c = 0, roots of cx” + bx + a = 0 are 1/α and 1/β.**if α and β are the roots of equation ax**^{2}+ bx + c = 0, roots of ax^{2}– bx + c = 0 are -α and -β.