(4/5a + 5/4b)²

asked by guest
on Nov 29, 2024 at 7:33 am



You asked:

Evaluate the expression: \({\left( \frac{4}{5 a} + \frac{5}{4 b} \right)}^{2}\)

MathBot Answer:

Evaluated



\(\displaystyle {\left( \frac{4}{5 a} + \frac{5}{4 b} \right)}^{2} = \left(\frac{5}{4 b} + \frac{4}{5 a}\right)^{2} \)


Expanded

\[{\left( \frac{4}{5 a} + \frac{5}{4 b} \right)}^{2} = \frac{25}{16 b^{2}} + \frac{2}{a b} + \frac{16}{25 a^{2}}\]


Factored

\[{\left( \frac{4}{5 a} + \frac{5}{4 b} \right)}^{2} = \frac{\left(25 a + 16 b\right)^{2}}{400 a^{2} b^{2}}\]