Question

factorise this equation
(729x^3-1)​

Answer 1

Step-by-step explanation:

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0+b3 =

a3+b3

Check : 729 is the cube of 9

Check : 1 is the cube of 1

Check : x3 is the cube of x1

Factorization is :

(9x - 1) • (81x2 + 9x + 1)

Trying to factor by splitting the middle term