Question

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

Answer 1

Solution:-
(64/125)a³ - 8 - (96/25)a² + (48/5)a
= (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)
= x³ - (2)³ -6x² + 12x (Putting 4a/5 = x)
= x³ - -6x² + 12x - (2)³
= x³ - (3*x²*2) + (3*x*2²) - (2)³  [(a-b)³ = a³ - 3a²b + 3ab² - b³]
= x³ - 6x(x-2) - (2)³  [(a-b)³ = a³ - 3ab(a-b) - b³]
= (x-2)³
= [(4a/5) - 2]³  (Putting x = 4a/5)
= (2³){(2a/5) - 1}³
=8{(2a - 5)/5}³
= 8/5³ (2a - 5)³
= (8/125) (2a - 5) (2a - 5) (2a - 5)
Answer.

Answer 2

Step-by-step explanation:

(64/125)a³ - 8 - (96/25)a² + (48/5)a

= (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)

= x³ - (2)³ -6x² + 12x (Putting 4a/5 = x)

= x³ - -6x² + 12x - (2)³

= x³ - (3*x²*2) + (3*x*2²) - (2)³  [(a-b)³ = a³ - 3a²b + 3ab² - b³]

= x³ - 6x(x-2) - (2)³  [(a-b)³ = a³ - 3ab(a-b) - b³]

= (x-2)³

= [(4a/5) - 2]³  (Putting x = 4a/5)

= (2³){(2a/5) - 1}³

=8{(2a - 5)/5}³

= 8/5³ (2a - 5)³

= (8/125) (2a - 5) (2a - 5) (2a-5)