((a^2+2ab+b^2)/b)×(((a-b)×(a+b))/ab)

asked by guest
on Oct 25, 2024 at 6:12 am



You asked:

Evaluate the expression: \(\frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b} = \frac{\left(a - b\right) \left(a + b\right) \left(a^{2} + 2 a b + b^{2}\right)}{b^{2} a} \)

Expanded

\[\frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b} = \frac{a^{3}}{b^{2}} + \frac{2 a^{2}}{b} - 2 b - \frac{b^{2}}{a}\]

Factored

\[\frac{{a}^{2} + 2 a b + {b}^{2}}{b} \cdot \frac{\left(a - b\right) \cdot \left(a + b\right)}{a b} = \frac{\left(a - b\right) \left(a + b\right)^{3}}{b^{2} a}\]

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