Question

(1/3b+a)(1/9b2-1/3ba+a2)-1/27b3

Answer 1

((1/3)b+a)((1/9)b²-(1/3)ba+a²)-(1/27)b³= ((1/3)b)³+ а³- ((1/3)b)³ = а³

Answer 2

To simplify the expression, let's break it down step by step:

1. Start with the expression:

   (1/3b + a)(1/9b^2 - 1/3ba + a^2) - 1/27b^3

2. Expand the first term (1/3b + a) using the distributive property:

   (1/3b)(1/9b^2 - 1/3ba + a^2) + a(1/9b^2 - 1/3ba + a^2) - 1/27b^3

3. Simplify each term individually:

   (1/27b^3 - 1/9b^2a + 1/3ba^2) + (1/9ab^2 - 1/3a^2b + a^3) - 1/27b^3

4. Combine like terms:

   (1/27b^3 - 1/9b^2a + 1/9ab^2) + (1/3ba^2 - 1/3a^2b + a^3) - 1/27b^3

5. The terms 1/27b^3 and -1/27b^3 cancel each other out:

   • 1/9b^2a + 1/9ab^2 + 1/3ba^2 - 1/3a^2b + a^3

Therefore, the simplified expression is: - 1/9b^2a + 1/9ab^2 + 1/3ba^2 - 1/3a^2b + a^3.