ABDULLAH EDUCATIONAL SOCIETYRegistered and Recognized

COMPOSED BY SIR AHTISHAM ALI

IMPORTANT MATH FORMULAS

FOR EXPANDING پھیلائو کیلیے For Find The Value: قیمت معلوم کرنے کیلیے1. (a+b )2=a2+2ab+b2 (a+b )2=a2+b2+2ab

2. (a−b )2=a2−2ab+b2 (a−b )2=a2+b2−2ab

3. (a+b )3=a3+3a2b+3ab2+b3 (a+b )3=a3+b3+3ab (a+b)

4. (a−b )3=a3−3a2b+3ab2−b3 (a−b )3=a3−b3−3 ab(a−b)

5. (a+b+c )2=a2+b2+c2+2ab+2bc+2ca For Expanding پھیلائو کیلیے

6. (a+b+c )2=a2+b2+c2+2(ab+bc+ca) قیمت معلوم کرنے کیلیے7. 2 (ab+bc+ca )=(a+b+c )2− (a2+b2+c2 ) ……………………………………

……

8. a2+b2+c2=(a+b+c )2−2(ab+bc+ca) For Find The Value:

9. a3+b3+c3−3abc=(a+b+c )(a2+b2+c2−ab−bc−ca)

10. 2 (a2+b2 )=(a+b )2+(a−b )2 11. 8ab (a2+b2 )=(a+b )4− (a−b )4

12. 4 ab=(a+b )2−(a−b )2 13. a2−b2= (a+b ) (a−b )

14. (x+ 1x )2

=x2+ 1x2

+2 x 1x

15. (x−1x )2

=x2+ 1x2

−2 x 1x

16. (x+ 1x )3

=x3+ 1x3

+3 x 1x (x+ 1x ) 17. (x−1x )

3

=x3− 1x3

−3x 1x(x−1

x)

For Factorization تجزی کےلیے18. a2+b2+2ab= (a+b )2 19. a2+b2−2ab=(a−b )2

20. a2−b2= (a+b ) (a−b ) 21. a4−b4=(a+b ) (a−b ) (a2+b2 )

22. a3+b3=(a+b ) (a2−ab+b2 ) 23. a3−b3=(a−b ) (a2+ab+b2 )

24. a6−b6=(a+b ) (a+b ) (a2−ab+b2 ) (a2+ab+b2 )

25. a3+b3+c3−3abc= (a+b+c ) (a2+b2+c2−ab−bc−ca )

26. a4+b4=(a2+b2−√2ab ) (a2+b2+√2ab ) Quadratic Formulaکلیہ درجی دو

27. (a4+a2+1 )=(a2−a+1 ) (a2+a+1 ) 28. x=−b±√b2−4ac2a

29. x2+ px+q=(x+a)(x+b) where p = a + b and q = ab