Question

evaulate:- (x-2y)^3 - (x+2y)^3​

Answer 1

Answer:

Step 1 :

1.1 Evaluate : (x-2y)3 = x3-6x2y+12xy2-8y3

1.2 Evaluate : (x+y)3 = x3+3x2y+3xy2+y3

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

-9x2y + 9xy2 - 9y3 = -9y • (x2 - xy + y2)

Trying to factor a multi variable polynomial :

2.2 Factoring x2 - xy + y2

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

Factorization fails

Final result :

-9y • (x2 - xy + y2)