Which of the following is the correct factorization of the polynomial below?

8x3 + 27y3

(2x + 3y) • (4x2 - 6xy + 9y2)

Step-by-step explanation:

Step 1:

Equation at the end of step 1:

(8 • (x3)) + 33y3

Step 2:

Equation at the end of step 2:

23x3 + 33y3

Step 3:

Trying to factor as a Sum of Cubes:

3.1 Factoring: 8x3+27y3

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 : 27 is the cube of 3

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is:

(2x + 3y) • (4x2 - 6xy + 9y2)