64m+n factorise the following
Answers
hi64m3+125n3
Final result :
(4m + 5n) • (16m2 - 20mn + 25n2)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(64 • (m3)) + 53n3
Step 2 :
Equation at the end of step 2 :
26m3 + 53n3
Step 3 :
Trying to factor as a Sum of Cubes :
3.1 Factoring: 64m3+125n3
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 : 64 is the cube of 4
Check : 125 is the cube of 5
Check : m3 is the cube of m1
Check : n3 is the cube of n1
Factorization is :
(4m + 5n) • (16m2 - 20mn + 25n2)
Trying to factor a multi variable polynomial :
3.2 Factoring 16m2 - 20mn + 25n2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
(4m + 5n) • (16m2 - 20mn + 25n2)
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