Factorise each of the following:
i) 27y³ + 125z³  ii) 64m³ - 343n³ 
[Hint: See Question 9]

Solution:

i) 27y³ + 125z³ = (3y)³ + (5z)³

Using factorization: (x³ + y³) = (x + y)(x² - xy + y²)

Here, x = 3y and y = 5z

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

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

ii) 64m³ - 343n³ = (4m)³ - (7n)³

Using factorization: (x³ - y³) = (x - y)(x² + xy + y²)

Here, x = 4m and y = 7n

(4m)³ - (7n)³ = (4m - 7n)[(4m)² + (4m)(7n) + (7n)²]

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

☛ Check: NCERT Solutions Class 9 Maths Chapter 2

Video Solution:

Factorise each of the following: i) 27y³ + 125z³ ii) 64m³ - 343n³ [Hint: See Question 9]

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.5 Question 10

Summary:

The factorized form of each of the following 27y³ + 125z³ and 64m³ − 343n³ are (3y + 5z)(9y² − 15yz + 25z²) and (4m  −7n)(16m² + 28mn + 49n²) respectively.

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