Question

what will be the factorisation of 64a^3b^3-27​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

(64 • (a3)) - 33b3

STEP

2

:

Equation at the end of step

2

:

26a3 - 33b3

STEP

3

:

Trying to factor as a Difference of Cubes

3.1 Factoring: 64a3-27b3

Theory : A difference 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 : 27 is the cube of 3

Check : a3 is the cube of a1

Check : b3 is the cube of b1