(450+280)^2-(450-280)^2/(450 x 280)

asked by guest
on Dec 28, 2024 at 6:54 am



You asked:

Evaluate the expression: \({\left( 450 + 280 \right)}^{2} - \frac{{\left( 450 - 280 \right)}^{2}}{450 \cdot 280}\)

MathBot Answer:

\[{\left( 450 + 280 \right)}^{2} - \frac{{\left( 450 - 280 \right)}^{2}}{450 \cdot 280} = \frac{671453711}{1260} = 532899.77\overline{063492}\]

\[\begin{aligned}{\left( 450 + 280 \right)}^{2} - \frac{{\left( 450 - 280 \right)}^{2}}{450 \cdot 280}& = \left(450 + 280\right)^{2} - \left(450 - 280\right)^{2} \cdot \frac{1}{450 \cdot 280}\\& = 730^{2} - \left(450 - 280\right)^{2} \cdot \frac{1}{450 \cdot 280}\\& = 532900 - \left(450 - 280\right)^{2} \cdot \frac{1}{450 \cdot 280}\\& = 532900 - 170^{2} \cdot \frac{1}{450 \cdot 280}\\& = 532900 - 28900 \cdot \frac{1}{450 \cdot 280}\\& = 532900 - \frac{28900}{126000}\\& = 532900 - \frac{289}{1260}\\& = \frac{671453711}{1260}\end{aligned}\]

+ Submit Question