Question

125a³+b³/216+25a²b/2+5ab²/12​

Answer 1

Answer:

$7 \times 3 - 2$

Answer 2

$\huge\mathcal\orange{Example}$

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