Factorise completely: 16m3 - 54n3
Answers
Answer:
16m3+54n3
Final result :
2 • (2m + 3n) • (4m2 - 6mn + 9n2)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "n3" was replaced by "n^3". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(16 • (m3)) + (2•33n3)
Step 2 :
Equation at the end of step 2 :
24m3 + (2•33n3)
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
16m3 + 54n3 = 2 • (8m3 + 27n3)
Trying to factor as a Sum of Cubes :
4.2 Factoring: 8m3 + 27n3
Theory : A sum 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 : 27 is the cube of 3
Check : m3 is the cube of m1
Check : n3 is the cube of n1
Factorization is :
(2m + 3n) • (4m2 - 6mn + 9n2)
Trying to factor a multi variable polynomial :
4.3 Factoring 4m2 - 6mn + 9n2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
2 • (2m + 3n) • (4m2 - 6mn + 9n2)
Answer:
2(2m-3n)(2m+6mn+3n)
Step-by-step explanation:
16m^3 - 54n^3
= 2(8m^3-27n^3)
= 2[(2m)^3 - 3n^3)]
= 2[(2m-3n)(2m+6mn+3n)]
{using identity a^3-b^3} =(a-b)(a+ab+b)
=2(2m-3n)(2m+6mn+3n)