Question

factorise 27a^3- 64+9a-12​

Answer 1

Answer:

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 : 27 is the cube of 3

Check : 64 is the cube of 4

Check : a3 is the cube of a1

Factorization is :

(3a + 4) • (9a2 - 12a + 16)