Question

: Factorise 8x³ + 27y3 +36x²y + 54xy²​

Answer 1

Topic :-

Factorisation

To Factorise :-

8x³ + 27y³ + 36x²y + 54xy²

Solution :-

8x³ + 27y³ + 36x²y + 54xy²

We can write :

--> 8x³ = (2x)³

--> 27y³ = (3y)³

--> 36x²y = 18xy(2x)

--> 54xy² = 18xy(3y)

Replacing values,

(2x)³ + (3y)³ + 18xy(2x) + 18xy(3y)

Taking '18xy' as common,

(2x)³ + (3y)³ + 18xy(2x + 3y)

We can rewrite it as,

(2x)³ + (3y)³ + 3(2x)(3y)(2x + 3y)

We can observe that it is similar to,

a³ + b³ + 3ab(a + b) = (a + b)³

Hence,

(2x)³ + (3y)³ + 3(2x)(3y)(2x + 3y) =

(2x + 3y)³

Answer :-

(2x + 3y)³

Additional Identities :-

a² + 2ab + b² = (a + b)²

a² - 2ab + b² = (a - b)²

a² - b² = (a + b)(a - b)

a³ - b³ - 3ab(a - b) = (a - b)³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)