Simplify:(a+b)3a−b . b(a+b)2

Answer 1

To simplify the expression \((a+b)3a - b \cdot b(a+b)^2\), let's break it down step by step.

1. Expand the first term \((a+b)3a\): \[ (a+b)3a = 3a(a+b) = 3a^2 + 3ab \]

2. Expand the second term \(-b \cdot b(a+b)^2\): \[ b(a+b)^2 = b(a^2 + 2ab + b^2) = ba^2 + 2bab + b^3 = ba^2 + 2ab^2 + b^3 \] Therefore, \[ -b(a+b)^2 = -ba^2 - 2ab^2 - b^3 \]

3. Combine the two expanded results: Now we can write the whole expression: \[ 3a^2 + 3ab - (ba^2 + 2ab^2 + b^3) \]

   Distributing the negative sign: \[ 3a^2 + 3ab - ba^2 - 2ab^2 - b^3 \]

4. Combine like terms: \[ (3a^2 - ba^2) + (3ab - 2ab^2) - b^3 \] This gives us: \[ (3 - b)a^2 + (3 - 2b)ab - b^3 \]

Thus, the simplified expression is:

\[ (3 - b)a^2 + (3 - 2b)ab - b^3 \]