Question

Factorise 8p^3-1^2/5 p^2 +6p/25-1/125

Answer 1

Given: The polynomial 8p^3 - 12/5p^2 + 6/25p - 1/125

To find: Factorise the given polynomial.

Solution:

Now we have provided with the polynomial 8p^3 - 12/5p^2 + 6/25p - 1/125.

So we can rewrite it as:

(2p)³ + 3 x (2p)² x 1/5 + 3 x 2p x (1/5)² + (1/5)³

Now we know the identity:

a³ + 3a²b + 3ab² + b³ = (a + b)³

(2p)³ + 3 x (2p)² x 1/5 + 3 x 2p x (1/5)² + (1/5)³ = (2p + 1/5)³

Answer:

So the factor of the polynomial 8p^3 - 12/5p^2 + 6/25p - 1/125 is (2p + 1/5)³.