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ES Important Formulas of Algebra, , This sheet comprises the algebra’s formulas that is being asked in all competitive exams recently. It was, prepared on the basis of my personal experience for Aspirants ‘convenience by me (your mentor). | hopefully, assume that it is very fruitful to each and every aspirant., , , , , , a? — b? = (a—b) (a? + ab + b’), , a? + b? = (a+ b) (a2— ab + b’), , (a+ b+ c)?=a? + b?+c?+ 3(atb) (b +c) (c+a), (a—b)*= (a+ b)?—4ab, , (a+b)? =(a—b)?+ 4ab, , a’+ b*= (a +b)?-2ab, , SN, , (a + b)? =a? + 3a*b + 3ab? + b?, (a + b)? = a3 + b? + 3ab (a+ b), a? + b?= (a + b)?— 3ab (a + b), (a—b)? = a3 — 3a*b + 3ab?— b?, (a—b)? = a? — b? — 3ab (a—b), a?—b? = (a—b)? + 3ab (a + b), , , , , , , , , , , , , , , > a? +b? +c?—3abc = (a + b+ c) (a2+ b? + c?— Mg—bi, , > |f(a+b+c) =O then, a? +b? +c? = 3abc, , > a? +b? +c? —3abe == (a + b+) [(a - D6 (c -a)?], > P4SrKC Babi alae BeBe + + be + ca)}, > a? +b? +c?—3abe == (a+ b+ -(a + b+ c)?}, , , , , , , , , , , , , 2 =(0't, , a? +b? E = [(a-b)?+ (b-c)? + (c-a)?], , ° tifa? +b be + ca or a? + b? +c? —ab—bc-—ca=0 then, (a=b=c), , e ita? +be+c*=0 then, (a=b=c=0); Suppose (x —a)?+ (y—b)?+ (z, en, (x=a, y=bandc=z), , b+c)(c+a) + abc =(a+b+c) (ab + be + ca), + b (c2- a?) + c (a*- b?) = (a—b) (b - c) (c- a), , , , , , , , , , , % If (a2 + ab +b’) =P and (a2—ab+b2)=Q, then a4+a*b?+b*=PxQ, , > If (a? — (a2-ab+b’)=Q, , -b, P+ and ab= a, , 14, , ity”, , then (a7+ b?) =, , “ If xy =1 then, =a