((a^(2)*b)-(a*b))*((a*b^(2))+ab)*(a+b)
You asked:
Evaluate the expression: \(\left({a}^{2} \cdot b - a b\right) \cdot \left(a \cdot {b}^{2} + a b\right) \cdot \left(a + b\right)\)
MathBot Answer:
Evaluated
\(\displaystyle \left({a}^{2} \cdot b - a b\right) \cdot \left(a \cdot {b}^{2} + a b\right) \cdot \left(a + b\right) = \left(a + b\right) \left(a^{2} b - a b\right) \left(b^{2} a + a b\right) \)
Expanded
\[\left({a}^{2} \cdot b - a b\right) \cdot \left(a \cdot {b}^{2} + a b\right) \cdot \left(a + b\right) = a^{4} b^{3} + a^{4} b^{2} + a^{3} b^{4} - a^{3} b^{2} - a^{2} b^{4} - a^{2} b^{3}\]
Factored
\[\left({a}^{2} \cdot b - a b\right) \cdot \left(a \cdot {b}^{2} + a b\right) \cdot \left(a + b\right) = a^{2} b^{2} \left(a - 1\right) \left(a + b\right) \left(b + 1\right)\]