Question

Factorise each of the following:
(i)27y³+125z³
(ii) 64m³-343n³

Answer 1

this is your first answer (i)

Answer 2

Answer:

27y³+125z³ = (3y + 5z) ( 9y² + 25z² - 15yz)

64m³-343n³ =  (4m - 7n) ( 16m² + 49n² + 28mn)

Step-by-step explanation:

27y³+125z³

= (3y)³ + (5z)³

using a³ + b³ = (a + b) (a² + b² - ab)

here a = 3y  & b = 5z

= (3y + 5z) ( (3y)² + (5z)² - (3y)(5z))

= (3y + 5z) ( 9y² + 25z² - 15yz)

27y³+125z³ = (3y + 5z) ( 9y² + 25z² - 15yz)

64m³-343n³

= (4m)³ + (-7n)³

now a = 4m  & b = - 7n

= ( 4m - 7n) ((4m)² + (-7n)² - (4m)(-7n))

= (4m - 7n) ( 16m² + 49n² + 28mn)

64m³-343n³ =  (4m - 7n) ( 16m² + 49n² + 28mn)