Question

(6m-n)(36m^2+6mn+n^2)-(3m+2n)^3​

Answer 1

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

((6m - n) • (((22•32m2) + 6mn) + n2)) - (3m + 2n)3

Step 2 :

Trying to factor a multi variable polynomial :

2.1 Factoring 36m2 + 6mn + n2

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

Factorization fails

Equation at the end of step 2 :

(6m - n) • (36m2 + 6mn + n2) - (3m + 2n)3

Step 3 :

3.1 Evaluate : (3m+2n)3 = 27m3+54m2n+36mn2+8n3

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

189m3 - 54m2n - 36mn2 - 9n3 =

9 • (21m3 - 6m2n - 4mn2 - n3)

Checking for a perfect cube :

4.2 21m3 - 6m2n - 4mn2 - n3 is not a perfect cube

Final result :

9 • (21m3 - 6m2n - 4mn2 - n3)

I hope this may help you

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