Question

Factorise

a⁶+b⁶

Answer 1

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 + b³can 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)

Processing ends successfully

I am done for a6-b6
Answer:

a6 - b6
= ( a3 )2 - ( a3 )2

= ( a3 - b​3 ) ( a3 + b3 )

= ( a - b ) ( a2 + ab + b2 ) ( a + b ) ( a2 - ab + b2 )