Question

Factorize:
8a³+27b³+36a²b+54ab²

Answer 1

Answer:

${a}^{3} + {b}^{3} + 3 {a}^{2}b + 3a {b}^{2} \\ = ( {a + b)}^{3}$

Step-by-step explanation:

(2a+3b)^3

Answer 2

The algebraic expression is given as : 8a³ + 27b³ + 36a²b + 54ab²

We can rewrite the  given expression as :  

= (2a)³ + (3b)³ + 3 × 2a × 3b(2a + 3b)

In order to factorise the given algebraic expression we use the following Identity - a³ + b³ + 3ab (a + b) = (a + b)³.

Here a = (2a) and b = (3b) :  

= (2a + 3b)³

= (2a + 3b)(2a + 3b)(2a + 3b)

Hence, the factorization of an algebraic expression is (2a + 3b)(2a + 3b)(2a + 3b).

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