Question

(e) (a? + b2 + c?) x (a – b + c)​

Answer 1

Answer:

How can you say einstein was not a bad people?

Answer 2

Answer:

Algebra

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

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

3. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

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

5. (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a − b)3 + 3ab(a − b)

6. a2 − b2 = (a + b)(a − b)

7. a3 − b3 = (a − b)(a2 + ab + b2)

8. a3 + b3 = (a + b)(a2 − ab + b2)

9. an − bn = (a − b)(an−1 + an−2b + an−3b2 + ··· + bn−1)

10. an = a.a.a . . . n times

11. am.an = am+n

12. am

an = am−n if m>n

= 1 if m = n

= 1

an−m if m<n; a ∈ R, a 6= 0

13. (am)n = amn = (an)m

14. (ab)n = an.bn

15. a

b

n

= an

bn

16. a0 = 1 where a ∈ R, a 6= 0

17. a−n = 1

an , an = 1

a−n

18. ap/q = √q ap

19. If am = an and a 6= ±1, a 6= 0 then m = n

20. If an = bn where n 6= 0, then a = ±b

21. If √x, √y are quadratic surds and if a + √x = √y, then a = 0 and x = y

22. If √x, √y are quadratic surds and if a+ √x = b+ √y then a = b and x = y

23. If a, m, n are positive real numbers and a 6= 1, then loga mn = loga m+loga n

24. If a, m, n are positive real numbers, a 6= 1, then loga

m

n

= loga m−loga n

25. If a and m are positive real numbers, a 6= 1 then loga mn = n loga m

26. If a, b and k are positive real numbers, b 6= 1, k 6= 1, then logb a = logk a

logk b

27. logb a = 1

loga b where a, b are positive real numbers, a 6= 1, b 6= 1

28. if a, m, n are positive real numbers, a 6= 1 and if loga m = loga n, then

m = n

29. if a + ib = 0 where i = √−1, then a = b = 0

30. if a + ib = x + iy, where i = √−1, then a = x and b = y

31. The roots of the quadratic equation ax2+bx+c = 0; a 6= 0 are −b ± √

b2 − 4ac

2a

The solution set of the equation is (

−b + √

∆

2a ,

−b − √

∆

2a

)

where ∆ = discriminant = b2 − 4ac

32. The roots are real and distinct if ∆ > 0.

33. The roots are real and coincident if ∆ = 0.

34. The roots are non-real if ∆ < 0.

35. If α and β are the roots of the equation ax2 + bx + c = 0, a 6= 0 then

i) α + β = −b

a = − coeff. of x

coeff. of x2

ii) α · β = c

a = constant term

coeff. of x2

36. The quadratic equation whose roots are α and β is (x − α)(x − β)=0

i.e. x2 − (α + β)x + αβ = 0

i.e. x2 − Sx + P = 0 where S =Sum of the roots and P =Product of the

roots.

37. For an arithmetic progression (A.P.) whose first term is (a) and the common

difference is (d).

i) nth term= tn = a + (n − 1)d

ii) The sum of the first (n) terms = Sn = n

2 (a + l) = n

2 {2a + (n − 1)d}

where l =last term= a + (n − 1)d.

38. For a geometric progression (G.P.) whose first term is (a) and common ratio

is (γ),

i) nth term= tn = aγn−1.

ii) The sum of the first (n) terms:

Sn = a(1 − γn)

1 − γ

ifγ < 1

= a(γn − 1)

γ − 1

if γ > 1

= na if γ = 1

.