A - B Whole Square : Solved Examples

(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)

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 A) (12a - 15b)2 Apply the value to identity i.e. (a - b)2 = a2 + b2 - 2ab (12a - 15b)2 = (12a)2 + (15b)2 - 2(12a)(15b) Solve the exponential forms = 144a2 + 225b2 - 2(12a)(15b) Solve multiplication process and we get: = 144a2 + 225b2 - 360ab Hence (12a - 15b)2 = 144a2 + 225b2 - 360ab B) (8x - 5y)2 Apply the value to identity i.e. (a - b)2 = a2 + b2 - 2ab (8x - 5y)2 = (8x)2 + (5y)2 - 2(8x)(5y) Solve the exponential forms = 64x2 + 25y2 - 2(8x)(5y) Solve multiplication process and we get: = 64x2 + 25y2 - 80xy Hence (8x - 5y)2 = 64x2 + 25y2 - 80xy C) (6x - 3y)2 Apply the value to identity i.e. (a - b)2 = a2 + b2 - 2ab (6x - 3y)2 = (6x)2 + (3y)2 - 2(6x)(3y) Solve the exponential forms = 36x2 + 9y2 - 2(6x)(3y) Solve multiplication process and we get: = 36x2 + 9y2 - 36xy Hence (6x - 3y)2 = 36x2 + 9y2 - 36xy D) (19x - 13y)2 Apply the value to identity i.e. (a - b)2 = a2 + b2 - 2ab (19x - 13y)2 = (19x)2 + (13y)2 - 2(19x)(13y) Solve the exponential forms = 361x2 + 169y2 - 2(19x)(13y) Solve multiplication process and we get: = 361x2 + 169y2 - 494xy Hence (19x - 13y)2 = 361x2 + 169y2 - 494xy Related Question 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