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 of identity first: Example 1: Solve (4p + 5q)2 Solution: This proceeds as: Given polynomial (4p + 5q)2 represents identity first i.e. (a + b)2 Where a = 4p and b = 5q Now apply values of a and b on the identity i.e. (a + b)2 = a2 + b2 + 2ab and we get: (4p + 5q)2 = (4p)2 + (5q)2 + 2(4p)(5q) Expand the exponential forms and we get: = 16p2 + 25q2 + 2(4p)(5q) Solve multiplication process and we get: = 16p2 + 25q2 + 40pq Hence, (4p + 5q)2 = 16p2 + 25q2 + 40pq Example 2: Solve (8x + 4y)2 Solution: This proceeds as: Given polynomial (8x + 4y)2 represents identity first i.e. (a + b)2 Where a = 8x and b = 4y Now apply values of a and b on the identity i.e. (a + b)2 = a2 + b2 + 2ab and we get: (8x + 4y)2 = (8x)2 + (4y)2 + 2(8x)(4y) Expand the exponential forms and we get: = 64x2 + 16y2 + 2(8x)(4y) Solve multiplication process and we get: = 64x2 + 16y2 + 64xy Hence, (8x + 4y)2 = 64x2 + 16y2 + 64xy Study More Solved Questions / Examples Solve the following equations by A + B Whole Square A) (22x + 27y)2 B) (14x + 7y)2 C) (15x + 9y)2 D) (18x + 4y)2 Solve the following equations by A + B Whole Square E) (9x + 3y)2 F) (13x + 7y)2 G) (16x + 7y)2