Question

factorise 24a3+81b3​

Answer 1

Answer:

3(2a+3b) (4a^2+9b^2-6ab)

Answer 2

Let us know some algebraic identity formulas before solving the problem:

(x + y)² = x² + 2xy + y²

(x - y)² = x² - 2xy + y²

(x + y)³ = x³ + 3x²y + 3xy² + y³

(x - y)³ = x³ - 3x²y + 3xy² - y³

x³ + y³ = (x + y) (x² - xy + y²)

x³ - y³ = (x - y) (x² + xy + y²)

Solution:

Now, 24a³ + 81b³

= 3 (8a³ + 27b³)

= 3 {(2a)³ + (3b)³}

= 3 (2a + 3b) {(2a)² - (2a × 3b) + (3b)²}

= 3 (2a + 3b) (4a² - 6ab + 9b²),

which is the required factorization.