Question

Factorise the following

(i) 3a³b-243ab³

(ii) x² - 625

(iii) a ³ +6³ +a+b

(iv) x (x - y)³ + 3x²y(x - y)​

Answer 1

Step-by-step explanation:

$(i) \: \: \: \: \: 3 {a}^{2} b - 243a {b}^{2} = 3ab(a - 81b). \\ \\ (ii) \: \: \: \: {x}^{2} - 625 \\ \\ = {x}^{2} - {25}^{2} \\ \\ = (x + 25)(x - 25). \\ \\ (iii) \: \: \: {a}^{3} + {b}^{3} + a + b = (a + b)( {a}^{2} - ab + {b}^{2} ) + (a + b) \\ \\ = (a + b)( {a}^{2} - ab + {b}^{2} + 1 ). \\ \\ \\ (iv) \\ \\ \\ \\ x {(x - y)}^{3} + 3 {x}^{2} y(x - y) \\ \\ = x(x - y) ({(x - y)}^{2} + 3 {x}^{}y )) \\ \\ = x(x - y)( {x}^{2} + {y}^{2} + xy) .$