6xy2 (3y-x) - 3x2 (x-3y) 2

Answer:6xy2 (3y-x) - 3x2 (x-3y) 2

Final result:

3x • (3y - x) • (x2 - 3xy - 2y2)

Step by step solution:

Step 1:

Equation at the end of step 1:

((6x• (y2)) • (3y-x)) - (3x2• (x-3y) 2)

Step 2:

Equation at the end of step 2:

((6x• (y2)) • (3y-x)) - 3x2• (x-3y) 2

Step 3:

Equation at the end of step 3:

((2•3xy2) • (3y - x)) - 3x2 • (x - 3y) 2

Step 4:

Equation at the end of step 4:

(2•3xy2) • (3y - x) - 3x2 • (x - 3y) 2

Step 5:

Pulling out like terms:

5.1 Pull out 3y-x

Note that x-3y = (-1) • 3y-x

After pulling out, we are left with:

(3y-x) • (2 • 3xy2 * (-1) + (3x2 * (x-3y)))

Step 6:

Pulling out like terms:

6.1 Pull out like factors:

3x3 - 9x2y - 6xy2 = 3x • (x2 - 3xy - 2y2)

Trying to factor a multi variable polynomial:

6.2 Factoring x2 - 3xy - 2y2

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

Factorization fails

Final result:

3x • (3y - x) • (x2 - 3xy - 2y2)