Question

factorise each of the following. 216 x cube -125 y cube

Answer 1

Hope it helps .............

Answer 2

216x³ - 125y³ = (6x - 5y)(36x² + 30xy + 25y²)

Given :

The expression 216x³ - 125y³

To find :

Factorise the expression

Formula :

a³ - b³ = (a - b)(a² + ab + b² )

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is 216x³ - 125y³

Step 2 of 2 :

Factorise the expression

We use the formula

a³ - b³ = (a - b)(a² + ab + b² )

Thus we get

216x³ - 125y³

$\sf = {(6x)}^{3} - {(5y)}^{3}$

$\sf = (6x - 5y) \{ \: {(6x)}^{2} - 6x.5y + {(5y)}^{2} \}$

= (6x - 5y)(36x² + 30xy + 25y²)

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