a+b3 - 8=a+b3 - 23=a+b-2a+b2 + 22 + a+b×2=a+b-2a2+b2+2ab+4 + 2a + 2b Using x3-y3 = x-yx2+y2+xy

factorise:(a+b)³-8

{(a + b)}^{3} - 8 = {(a + b)}^{3} - {(2)}^{3} = (a + b - 2) [{(a + b)}^{2} + {(2)}^{2} + (a + b) \times 2] = (a + b - 2) [a^{2} + b^{2} + 2 ab + 4 + 2 a + 2 b] [Using x^{3} - y^{3} = (x - y) (x^{2} + y^{2} + xy)]

factorise:(a+b)3-8