Question

Factorise:- (2a+3)^3+(3a-2)^3-(5a+1)^3

Answer 1

Heres your answer

$(2a + 3) ^{3} + (3a - 2) ^{3} - (5a + 1) ^{3} \\ \\ as \: using\: the \: identity \: \\ \\ (8{a}^{3} + 27 + 36 {a}^{2} + 54a) + (27 {a}^{3} - 8 - 54 {a}^{2} + 36a) - \\ (125 {a}^{3} + 1 + 75 {a}^{2} + 15a) \\ \\ 8 {a}^{3} + 27 + 36 {a}^{2} + 54a + 27 {a}^{3} - 8 - 54 {a}^{2} + 36a \\ - 125 {a}^{3} - 1 - 75 {a}^{2} - 15a \\ \\ = 35 {}^{3} - 125 {a}^{3} + 19 - 1 - 18 {a}^{2} - 75 {a}^{2} + 90a - 15a \\ \\ = - 90 {a}^{3} + 18 - 93 {a}^{2} + 75a$

Hope it Helps!!