(A - B) Cube : 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 using (A - B) Cube formula A) (2x - 3y)3 B) (5x - 4y)3 C) (9x - 5y)3 D) (13x - 7y)3 E) (15x - 9y)3 F) (17x - 11y)3 G) (19x - 13y)3 A) (2x - 3y)3 Apply the value to identity i.e. (a - b)3 = a3 - b3 - 3a2b + 3ab2 (2x - 3y)3 = (2x)3 - (3y)3 - 3(2x)2 (3y) + 3(2x)(3y)2 Solve the exponential forms = 8x3 - 27y3 - 3(4x2) (3y) + 3(2x)(9y2) Solve multiplication process and we get: = 8x3 - 27y3 - 36x2y + 54xy2 Hence (2x - 3y)3 = 8x3 - 27y3 - 36x2y + 54xy2 B) (5x - 4y)3 Apply the value to identity i.e. (a - b)3 = a3 - b3 - 3a2b + 3ab2 (5x - 4y)3 = (5x)3 - (4y)3 - 3(5x)2 (4y) + 3(5x)(4y)2 Solve the exponential forms = 125x3 - 64y3 - 3(25x2) (4y) + 3(5x)(16y2) Solve multiplication process and we get: = 125x3 - 64y3 - 300x2y + 240xy2 Hence (5x - 4y)3 = 125x3 - 64y3 - 300x2y + 240xy2 C) (9x - 5y)3 Apply the value to identity i.e. (a - b)3 = a3 - b3 - 3a2b + 3ab2 (9x - 5y)3 = (9x)3 - (5y)3 - 3(9x)2 (5y) + 3(9x)(5y)2 Solve the exponential forms = 729x3 - 125y3 - 3(81x2) (5y) + 3(9x)(25y2) Solve multiplication process and we get: = 729x3 - 125y3 - 1215x2y + 675xy2 Hence (9x - 5y)3 = 729x3 - 125y3 - 1215x2y + 675xy2 D) (13x - 7y)3 Apply the value to identity i.e. (a - b)3 = a3 - b3 - 3a2b + 3ab2 (13x - 7y)3 = (13x)3 - (7y)3 - 3(13x)2 (7y) + 3(13x)(7y)2 Solve the exponential forms = 2197x3 - 343y3 - 3(169x2) (7y) + 3(13x)(49y2) Solve multiplication process and we get: = 2197x3 - 343y3 - 3549x2y + 1911xy2 Hence (13x - 7y)3 = 2197x3 - 343y3 - 3549x2y + 1911xy2 E) (15x - 9y)3 Apply the value to identity i.e. (a - b)3 = a3 - b3 - 3a2b + 3ab2 (15x - 9y)3 = (15x)3 - (9y)3 - 3(15x)2 (9y) + 3(15x)(9y)2 Solve the exponential forms = 3375x3 - 729y3 - 3(225x2) (9y) + 3(15x)(81y2) Solve multiplication process and we get: = 3375x3 - 729y3 - 6075x2y + 3645xy2 Hence (15x - 9y)3 = 3375x3 - 729y3 - 6075x2y + 3645xy2 F) (17x - 11y)3 Apply the value to identity i.e. (a - b)3 = a3 - b3 - 3a2b + 3ab2 (17x - 11y)3 = (17x)3 - (11y)3 - 3(17x)2 (11y) + 3(17x)(11y)2 Solve the exponential forms = 4913x3 - 1331y3 - 3(289x2) (11y) + 3(17x)(121y2) Solve multiplication process and we get: = 4913x3 - 1331y3 - 9537x2y + 6171xy2 Hence (17x - 11y)3 = 4913x3 - 1331y3 - 9537x2y + 6171xy2 G) (19x - 13y)3 Apply the value to identity i.e. (a - b)3 = a3 - b3 - 3a2b + 3ab2 (19x - 13y)3 = (19x)3 - (13y)3 - 3(19x)2 (13y) + 3(19x)(13y)2 Solve the exponential forms = 6859x3 - 2197y3 - 3(361x2) (13y) + 3(19x)(169y2) Solve multiplication process and we get: = 6859x3 - 2197y3 - 14079x2y + 9633xy2 Hence (19x - 13y)3 = 6859x3 - 2197y3 - 14079x2y + 9633xy2 Related Question Examples Solve the following equations using (A - B) Cube formula A) (2x - 3y)3 B) (5x - 4y)3 C) (9x - 5y)3 D) (13x - 7y)3 E) (15x - 9y)3 F) (17x - 11y)3 G) (19x - 13y)3