" 7."a^(3)x^(3)-3a^(2)bx^(2)+3ab^(2)x-b^(3)

Factorize: a^(3)x^(3)-3a^(2)bx^(2)+3ab^(2)x-b^(3)

Factorise a^3x^3-3a^2bx^2+3ab^2x-b^3

Factorize: a^3x^3-3a^2b x^2+3a b^2x-b^3

Write down each of the following in exponential form: 4a^(3)x6ab^(2)xc^(2) (ii) 5xyx3x^(2)yx7y^(2)a^(3)x3ab^(2)x2a^(2)b^(2)

For any a,b,c,x,y>0 prove that :(2)/(3)tan^(-1)((3ab^(2)-a^(3))/(b^(3)-3a^(2)b))+(2)/(3)tan^(-1)((3xy^(2)-x^(3))/(y^(3)-3x^(2)y))=tan^(-1)(2 alpha beta)/(a^(2)-beta^(2)) where alpha=-ax+by,beta=bx+ay

a^(2)b^(3)x2ab^(2) is equal to: 2a^(3)b^(4)(b)2a^(3)b^(5)(c)2ab (d) a^(3)b^(5)

a^(3)+3a^(2)b+3ab^(2)+b^(3) divided by a^(2)+2ab+b^(2) is

If c^(2) != ab and the roots of (c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac)+0 are equal show that a^(3)+b^(3)+c^(3)=3abc (or) a = 0.

If c^(2) ne ab and the roots of (c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac)=0 are equal, then show that a^(3)+b^(3)+c^(3)=3abc" or "a=0