Question

(A-2b) (a+b) ^2 +(a-b) ^3 +3b^3

Answer 1

Пошаговое объяснение:

(a-2b)(a²+2ab+b²)+(a³-3a²b+3ab²-b³)+3b³=

a³+2a²b+ab²-2a²b-4ab²-2b³+a³-3a²b+3ab²-b³+3b³=

=2a³-3a²b

Answer 2

Let's simplify the expression (A-2b)(a+b)^2 + (a-b)^3 + 3b^3 step by step:

1. Start with (a+b)^2: (a+b)^2 = a^2 + 2ab + b^2

2. Next, multiply this result by (A-2b): (A-2b)(a^2 + 2ab + b^2) = A(a^2 + 2ab + b^2) - 2b(a^2 + 2ab + b^2)

3. Distribute the terms on the right side: Aa^2 + 2Aab + Ab^2 - 2ba^2 - 4b^2a - 2b^3

4. Now, let's move to the next term, (a-b)^3: (a-b)^3 = (a-b)(a-b)^2

5. Calculate (a-b)^2: (a-b)^2 = a^2 - 2ab + b^2

6. Now, multiply this result by (a-b): (a-b)(a^2 - 2ab + b^2) = a(a^2 - 2ab + b^2) - b(a^2 - 2ab + b^2)

7. Distribute the terms on the right side: a^3 - 2a^2b + ab^2 - a^3 + 2ab^2 - b^3

8. Combine like terms: -2a^2b + 3ab^2 - b^3

9. Finally, add the third term, 3b^3.

Now, you can add the results from steps 3, 8, and the third term together:

Aa^2 + 2Aab + Ab^2 - 2ba^2 - 4b^2a - 2b^3 - 2a^2b + 3ab^2 - b^3 + 3b^3

Now, let's simplify by combining like terms:

Aa^2 - 2ba^2 - 2a^2b + 2Aab + 3ab^2 + Ab^2 + 3b^3 - b^3 - 4b^2a

Combine like terms:

(A - 2b - 2a + 2A)a^2 + (2A - 2 - 4b + 3)a*b + (3 - 1)b^3

Now, you have a simplified expression:

(A - 2a - 2b + 2A)a^2 + (2A - 2 - 4b + 3)ab + 2b^3