Question

27x^ 3 +8y^ 3 +z^ 3 -18xyz​

Answer 1

step 1

(27 • (x3)) + (23y3 • z3)

STEP

2

:

Equation at the end of step

2

:

33x3 + 23y3z3

STEP

3

:

Trying to factor as a Sum of Cubes

3.1 Factoring: 27x3+8y3z3

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 : 8 is the cube of 2

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Check : z3 is the cube of z1

Factorization is :

(3x + 2yz) • (9x2 - 6xyz + 4y2z2)

Trying to factor a multi variable polynomial :

3.2 Factoring 9x2 - 6xyz + 4y2z2

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

Factorization fails

Final result :

(3x + 2yz) • (9x2 - 6xyz + 4y2z2

Answer 2

Step-by-step explanation:

[(3x)+(2y)+(z)](9x²+4y²+z²-6xy-4y-6x