The product `(a+b)(a-b)(a^2-a b+b^2)(a^2+a b+b^2)` is equal to:
(a)`a^6+b^6`
(b) `a^6-b^6`
(c) `a^3-b^3`
(d) `a^3+b^3`

a^2b^3\ X\ 2a b^2 is equal to: (a) 2a^3b^4 (b) 2a^3b^5 (c) 2a b (d) a^3b^5

a^3 x 2a^2b x 3a b^5 is equal to: (a) a^6b^6 (b) 23 a^6b^6 (c) 6a^6b^6 (d) None of these

4 a 2 b 3 x 3a b 2 x 5 a 3 b is equal to: (a) 60 a 3 b 5 (b) 60 a 6 b 5 (c) 60 a 6 b 6 (d) a 6 b 5

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

Simplify: 4a b(a-b)-6a^2(b-b^2)-3b^2(2a^2-a)+2a b(b-a)

Find the product: (2a-3b-2c)(4\ a^2+\ 9\ b^2+\ 4\ c^2+\ 6\ a b-6\ b c+4c a)

The common difference of the A.P. 1/(2b),(1-6b)/(2b),(1-12 b)/(2b),... is (a) 2b (b) -2b (c) 3 (d) -3

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If a,b, c are real and distinct numbers, then the value of ((a-b)^(3)+(b-c)^(3)+(c-a)^(3))/((a-b).(b-c).(c-a))is

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

Factorise : 12abc -6a^(2) b^(2) c^(2) + 3a^(3) b^(3) c^(3)