Factorise 64/125a^3-96/25a^2+48/5a-8

Given equation

(64/125)a³ – 8 – (96/25)a² + (48/5)a

We will simply and write in the cube format
= (4/5)³a³ – (2)³ – 6(4/5)²a² + 12(4/5)a
=(4a/5)³ – (2)³ – 6*(4a/5)² + 12(4a/5)—————(1)

We will assume 4a/5 = x

Substituting the assumed value of x in equation (1)
= x³ – (2)³ -6x² + 12x
= x³ – -6x² + 12x – (2)³ ————–(2)

The above equation is the form of the identity (a-b)³

(a-b)³ = a³ – 3a²b + 3ab² – b³

Expressing the equation (2) as per the identity, we get
= x³ – (3*x²*2) + (3*x*2²) – (2)³ ———(3)

The equation 3 is the form of [(a-b)³ = a³ – 3ab(a-b) – b³]

Simplyfing as per the above identity, we get
= x³ – 6x(x-2) – (2)³
= (x-2)³

Putting x = 4a/5 we get
= [(4a/5) – 2]³

Taking out 2 as a common factor
= (2³){(2a/5) – 1}³
=8{(2a – 5)/5}³
= 8/5³ (2a – 5)³
= (8/125) (2a – 5) (2a – 5) (2a – 5)

= (8/125) (2a – 5)³

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