125a³+b³/216+25a²b/2+5ab²/12
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Factorise 64/125a^3-96/25a^2+48/5a-8
Given equation
64/125a³ – 8 – 96/25a² + 48/5a
We will simply and write in the cube format
= 4/5³a³ – 2³ – 64/5²a² + 124/5a
=4a/5³ – 2³ – 6*4a/5² + 124a/5—————1
We will assume 4a/5 = x
Substituting the assumed value of x in equation 1
= x³ – 2³ -6x² + 12x
= x³ – -6x² + 12x – 2³ ————–2
The above equation is the form of the identity a−b³
a−b³ = a³ – 3a²b + 3ab² – b³
Expressing the equation 2 as per the identity, we get
= x³ – 3∗x²∗2 + 3∗x∗2² – 2³ ———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 – 6xx−2 – 2³
= x−2³
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–5³
= 8/125 2a–5 2a–5 2a–5
= 8/125 2a–5³
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