" (iii) "q^(2)b(a-b^(2))+ab^(2)(4ab-2a^(2))-a^(3)b(1-2b)

Simplify: a^(2)b(a-b^(2))+ab^(2)(4ab-2a^(2))-a^(3)b(1-2b)

Simplify each of the following a^(2)b(a - b^(2)) + ab^(2)(4ab - 2a^(2)) - a^(3)b(1-2b)

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

Simplify : 6a^(2)+3ab+5b^(2)-2ab-b^(2)+2a^(2)+4ab+2b^(2)-a^(2) .

Prove that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

If a and b are real and i=sqrt(-1) then sin[i ln((a+ib)/(a-ib))] is equal to 1) (2ab)/(a^(2)-b^(2)) 2) (-2ab)/(a^(2)-b^(2)) 3) (2ab)/(a^(2)+b^(2)) 4) (-2ab)/(a^(2)+b^(2))

Simplify: a^(2)b(a^(3)-a+1)-ab(a^(4)-2a^(2)+2a)-b(a^(3)-a^(2)-1)

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 x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is

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 x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is