Question

factorise 125a³- 8b³​

Answer 1

It can be written as (5a)^3 - (2b)^3

Using the identity,

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

we get,

125a^3 - 8b^3 = (5a - 2b)(25a^2 + 10ab + 4b^2)

Answer 2

On factoring 125a³- 8b³​ we will get (5a-2b)(25a² +10ab +4b²)

Given problem:

Factorise 125a³- 8b³​

Solution:

Given 125a³- 8b³​

As we know

125 = 5³ ⇒  125a³ = (5a)³  

8 = 2³ ⇒ 8b³​ = (2b)³

From above,

125a³- 8b³​ = (5a)³- (2b)³  

We know that from algebraic identities

              (a³-b³) = (a-b)(a²+ab +b²)

Take a = 5a and b = 2b and apply above formula

(5a)³- (2b)³ = (5a-2b)[ (5a)² +(5a)(2b) + (2b)² ]

                   = (5a-2b)(25a² +10ab +4b²)  

⇒ 125a³- 8b³​ = (5a-2b)(25a² +10ab +4b²)

Therefore,

On factoring 125a³- 8b³​ we will get (5a-2b)(25a² +10ab +4b²)

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