A Square - B Square

(a + b)2 = a2 + b2 + 2ab	(a - b)2 = a2 + b2 - 2ab	a2 - b2 = (a + b) (a - b)	(x + a) (x + b) = x2 + x(a + b) + ab	(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a + b)3 = a3 + b3 + 3ab(a + b)	(a - b)3 = a3 - b3 - 3ab(a - b)	a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)

Before you understand A Square - B Square : a2 - b2 = (a + b) (a - b), you are advised to read: How to Multiply Variables ? How to Multiply Polynomials ? What is Exponential Form ? How this identity of a2 - b2 = (a + b) (a - b) is obtained: Taking RHS of the identity: (a + b) (a - b) Multiply as we do multiplication of two binomials and we get: = a(a - b) + b(a - b) = a2 - ab + ab - b2 Solve like terms and we get: = a2 - b2 Hence, in this way we obtain the identity i.e. a2 - b2 = (a + b) (a - b) Following are few applications of this identity. Example 1: Solve 3a2 - 2b2 Solution: This proceeds as: Given polynomial 3a2 - 2b2 represents identity third i.e. a2 - b2 Where a = 3a and b = 2b Now apply values of a and b on the identity i.e. a2 - b2 = (a + b) (a - b) and we get: 3a2 - 2b2 = (3a + 2b) (3a - 2b) Hence, 3a2 - 2b2 = (3a + 2b) (3a - 2b) Example 2: Solve (6m + 9n) (6m - 9n) Solution: This proceeds as: Given polynomial (6m + 9n) (6m - 9n) represents identity third i.e. a2 - b2 Where a = 6m and b = 9n Now apply values of a and b on the identity i.e. a2 - b2 = (a + b) (a - b) and we get: (6m + 9n) (6m - 9n) = (6m)2 - (9n)2 Expand the exponential forms on the LHS and we get: = 36m2 - 81n2 Hence, (6m + 9n) (6m - 9n) = 36m2 - 81n2