factorize. 64 a6–b6
Answers
Answer:
a6+b6
Final result :
(a2 + b2) • (a4 - a2b2 + b4)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "b6" was replaced by "b^6". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Trying to factor as a Sum of Cubes :
1.1 Factoring: a6+b6
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 : a6 is the cube of a2
Check : b6 is the cube of b2
Factorization is :
(a2 + b2) • (a4 - a2b2 + b4)
Trying to factor a multi variable polynomial :
1.2 Factoring a4 - a2b2 + b4
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Final result :
(a2 + b2) • (a4 - a2b2 + b4)