Question

factorise fully n simplify where possible 8a^6+729​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

23a6 + 729

STEP

2

:

Trying to factor as a Sum of Cubes:

2.1 Factoring: 8a6+729

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 : 729 is the cube of 9

Check : a6 is the cube of a2

Factorization is :

(2a2 + 9) • (4a4 - 18a2 + 81)