Question

Using a suitable identity factorize 64m cubed-343n cubed.

Answer 1

64m3-343n3 Final result : (4m - 7n) • (16m2 + 28mn + 49n2)

Step by step solution :Step  1  :Equation at the end of step  1  : (64 • (m3)) - 73n3 Step  2  :Equation at the end of step  2  : 26m3 - 73n3 Step  3  :Trying to factor as a Difference of Cubes:

 3.1      Factoring:  64m3-343n3 

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 :  64  is the cube of  4 

Check :  343  is the cube of   7 
Check :  m3 is the cube of   m1

Check :  n3 is the cube of   n1

Factorization is :
             (4m - 7n)  •  (16m2 + 28mn + 49n2) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    16m2 + 28mn + 49n2 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result : (4m - 7n) • (16m2 + 28mn + 49n2)

Processing ends successfully