`(2a+3b)^3`=`(2a)^3+(3b)^3+3.2a.3b(2a+3b)`

i) (2a-3b)^3

Factorize: 4\ (x+y)^2-28 y(x+y)+49 y^2 (2a+3b)^2+2(2a+3b)(2a-3b)+(2a-3b)^2

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

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

Simplify each of the following: -5(a+b)+2(2a-b)+4a-7 -3(a+b)+4(2a-3b)-(2a-b)

Evaluate : (i) ((a)/(2b)+(2b)/(a))^(2)-((a)/(2b)-(2b)/(a))^(2)-4 (ii) (4a+3b)^(2)-(4a-3b)^(2)+48ab

The value of [{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3}/{(a-b)^3+(b-c)^3+(c-a)^3}] = (1) 3(a+b)(b+c)(c+a) (2) 3(a-b)(b-c)(c-a) (3) (a+b)(b+c)(c+a) (4) 1

Evaluate: (2a + 3b)^(3)

Factorise : (iv) 8 (2a + 3b)^(3) - 12 (2a + 3b)^2

Simplify: ((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a)^3)