Question

B) Factorise. 8a³ – 27b³​

Answer 1

Answer:

$\sf 8a^3 - 27b^3 = (2a - 3b)(4a^2 + 6ab + 9b^2)$

Step-by-step explanation:

Algebraic identities:

We can use the algebraic identities, to factorize the expression.

      $\boxed{\bf x^3 - y^3 = (x - y)(x^2 + xy +y^2)}$

$\sf 8a^3 = 2^3 *a^3 = (2a)^3\\\\27b^3 = 3^3b^3 = (3b)^3$

x = (2a)³  and y = (3b)³

$\sf 8a^3 - 27b^3 = (2a)^3 - (3b)^3$

                 $\sf = (2a - 3b)( (2a)^2 + 2a * 3b + (3b)^2)\\\\= (2a - 3b) (4a^2 + 6ab + 9b^2)$