Question

Factorize the equation:
8x^3 - 37​

Answer 1

Step-by-step explanation:

23x3

37Factoring:  8x3-37 

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 :  8  is the cube of  2 

Check :  37  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes