Question

(8a^3 - 27b^3) × (4a^2 - 6ab + 9b^2) (2a+3b)​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

STEP

2

:

Equation at the end of step

2

:

STEP

3

:

8a3 - 27b3

Simplify ——————————

2a - 3b

Trying to factor as a Difference of Cubes:

3.1 Factoring: 8a3 - 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 : 8 is the cube of 2

Check : 27 is the cube of 3

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Factorization is :

(2a - 3b) • (4a2 + 6ab + 9b2)

Trying to factor a multi variable polynomial :

3.2 Factoring 4a2 + 6ab + 9b2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Canceling Out :

3.3 Cancel out (2a - 3b) which appears on both sides of the fraction line.

Final result :

4a2 + 6ab + 9b2