Question

Q.9 Factorise
27y³ + 125z³​

Answer 1

Answer:

(i) 27y³ + 125z³

We know that,

x³ + y³ = (x+y) ( x² - xy + y² )

So, here

x = 3y , y = 5z

= 27y³ + 125z³ = (3y + 5z) { (3y)² - 3y*5x + (5z)² }

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

➖➖➖➖➖➖➖➖➖➖➖

(ii) 64m³ - 343n³

We know that,

x³ - y³ = (x-y) ( x² - xy + y² )

So, here

x = 4m , y = 7n

= 64m³ - 343n³ = (4m - 7n) { (4m)² + 4m*7n + (7n)² }

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

Answer 2

Answer :

• (3y + 5z) (9y + 25z² - 15yz)

Given :

• 27xy³ + 125z³

Solution :

As we know that ,

• a³ + b³ = (a + b) (a² - ab + b²)

where a = 3y and b = 5z

⇢ (3y + 5z) [ (3y)² + (5z)² - (3y) (5z)]

⇢ (3y + 5z) (9y + 25z² - 15yz)

Hence, 27xy³ + 125z³ = (3y + 5z) (9y + 25z² - 15yz)

More Explanation :

• a² + b² = (a + b) (a - b)

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a³ + b³ = (a + b) (a² - ab + b²)

• a³ - b³ = (a -b) (a² + ab + b²)