Question

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

Answer 1

Answer:

19a3 - 35b3

Step-by-step explanation:

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

Step 2 :

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

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

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

Step 5 :

• (3a-2b)•((32a2+6ab)+22b2))-(2a+3b)•(4a2-6ab+9b2)
• 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 !!
• Ruling : Binomial can not be factored as the difference of two perfect cubes
• Final result :
• 19a3 - 35b3
• hope this will help you.So I am requesting you please mark me as a brainlist please.