Question

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

Answer 1

Answer:

The given expression can be written as

8x³ + 36x²y + 54xy²+ 27y³

= (2x)³ + 3(2x)² (3y) + 3(2x) (3y)² + (3y)³

Comparing with Identity VI,

(x + y)³ = x³ + 3x²y + 3xy² + y³

we get = (2x + 3y)³

= (2x + 3y) (2x + 3y) (2x + 3y).

Answer 2

Answer:

8x3−27y3−36x2y+54xy2

=(2x)3−(3y)3−3×(2x)2×3y+3×2x×(3y)2

Using,(a−b)3=a3−b3−3a2b+3ab2

=(2x−3y)3

=(2x−3y)(2x−3y)(2x−3y)

Step-by-step explanation:

8x3−27y3−36x2y+54xy2

=(2x)3−(3y)3−3×(2x)2×3y+3×2x×(3y)2

Using,(a−b)3=a3−b3−3a2b+3ab2

=(2x−3y)3

=(2x−3y)(2x−3y)(2x−3y)