A - B Whole 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 - B Whole Square : (a - b)2 = a2 + b2 - 2ab, you are advised to read: How to Multiply Variables ? How to Multiply Polynomials ? What is Exponential Form ? How this identity of (a - b)2 = a2 + b2 - 2ab is obtained: Taking LHS of the identity: (a - b)2 This can also be written as: = (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 Add like terms and we get: = a2 - 2ab + b2 Rearrange the terms and we get: = a2 + b2 - 2ab Hence, in this way we obtain the identity i.e. (a - b)2 = a2 + b2 - 2ab Following are few applications this identity. Example 1: Solve (3a - 2b)2 Solution: This proceeds as: Given polynomial (3a - 2b)2 represents identity second i.e. (a - b)2 Where a = 3a and b = 2b Now apply values of a and b on the identity i.e. (a - b)2 = a2 + b2 - 2ab and we get: (3a - 2b)2 = (3a)2 + (2b)2 - 2(3a)(2b) Expand the exponential forms and we get: = 9a2 + 4b2 - 2(3a)(2b) Solve multiplication process and we get: = 9a2 + 4b2 - 12ab Hence, (3a - 2b)2 = 9a2 + 4b2 - 12ab Example 2: Solve (6m - 9n)2 Solution: This proceeds as: Given polynomial (6m - 9n)2 represents identity second i.e. (a - b)2 Where a = 6m and b = 9n Now apply values of a and b on the identity i.e. (a - b)2 = a2 + b2 - 2ab and we get: (6m - 9n)2 = (6m)2 + (9n)2 - 2(6m)(9n) Expand the exponential forms and we get: = 36m2 + 81n2 - 2(6m)(9n) Solve multiplication process and we get: = 36m2 + 81n2 - 108mn Hence, (6m - 9n)2 = 36m2 + 81n2 - 108mn Study More Solved Questions / Examples Solve the following equations by using A - B Whole Square A) (12a - 15b)2 B) (8x - 5y)2 C) (6x - 3y)2 D) (19x - 13y)2 Solve the following equations by using A - B Whole Square A) (11x - 7y)2 B) (9a - 4b)2 C) (19x - 7y)2 D) (16x - 4y)2