Question

Simplify (3a-2b)(9a^2 +6ab+4b^2) + (2a+3b)^3

Answer 1

Answer:

Step-by-step explanation:Step 1 :

Equation at the end of step 1 :

((3a-2b)•(((9•(a2))-6ab)+(4•(b2))))-((2a+3b)•(((4•(a2))-6ab)+32b2))

Step 2 :

Equation at the end of step 2 :

((3a-2b)•(((9•(a2))-6ab)+(4•(b2))))-((2a+3b)•((22a2-6ab)+32b2))

Step 3 :

Trying to factor a multi variable polynomial :

3.1 Factoring 4a2 - 6ab + 9b2

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

Factorization fails

Equation at the end of step 3 :

((3a-2b)•(((9•(a2))-6ab)+(4•(b2))))-(2a+3b)•(4a2-6ab+9b2)

Step 4 :

Equation at the end of step 4 :

((3a-2b)•(((9•(a2))-6ab)+22b2))-(2a+3b)•(4a2-6ab+9b2)

Step 5 :

Equation at the end of step 5 :

((3a-2b)•((32a2-6ab)+22b2))-(2a+3b)•(4a2-6ab+9b2)

Step 6 :

Trying to factor a multi variable polynomial :

6.1 Factoring 9a2 - 6ab + 4b2

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

Factorization fails

Equation at the end of step 6 :

(3a-2b)•(9a2-6ab+4b2)-(2a+3b)•(4a2-6ab+9b2)

Step 7 :

Checking for a perfect cube :

7.1 19a3-36a2b+24ab2-35b3 is not a perfect cube

Final result :

19a3 - 36a2b + 24ab2 - 35b3

Answer 2

Answer:

 19a3 - 35b3

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((3a-2b)•(((9•(a2))+6ab)+(4•(b2))))-((2a+3b)•(((4•(a2))-6ab)+32b2))

Step  2  :

Equation at the end of step  2  :

 ((3a-2b)•(((9•(a2))+6ab)+(4•(b2))))-((2a+3b)•((22a2-6ab)+32b2))

Step  3  :

Trying to factor a multi variable polynomial :

3.1    Factoring    4a2 - 6ab + 9b2  

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

Factorization fails

Equation at the end of step  3  :

 ((3a-2b)•(((9•(a2))+6ab)+(4•(b2))))-(2a+3b)•(4a2-6ab+9b2)

Step  4  :

Equation at the end of step  4  :

 ((3a-2b)•(((9•(a2))+6ab)+22b2))-(2a+3b)•(4a2-6ab+9b2)

Step  5  :

Equation at the end of step  5  :

 ((3a-2b)•((32a2+6ab)+22b2))-(2a+3b)•(4a2-6ab+9b2)

Step  6  :

Trying to factor a multi variable polynomial :

6.1    Factoring    9a2 + 6ab + 4b2  

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

Factorization fails

Equation at the end of step  6  :

 (3a-2b)•(9a2+6ab+4b2)-(2a+3b)•(4a2-6ab+9b2)

Step  7  :

Trying to factor as a Difference of Cubes:

7.1      Factoring:  19a3-35b3  

Theory : A difference 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 :  19  is not a cube !!