$\left(1.5x-0.5y\right)^{2}-\left(0.5x-1.5y\right)^{2}$
You asked:
Evaluate the expression: \({\left( 1.5 x - 0.5 y \right)}^{2} - {\left( 0.5 x - 1.5 y \right)}^{2}\)
MathBot Answer:
Evaluated
\(\displaystyle {\left( 1.5 x - 0.5 y \right)}^{2} - {\left( 0.5 x - 1.5 y \right)}^{2} = - \left(\frac{x}{2} - \frac{3 y}{2}\right)^{2} + \left(\frac{3 x}{2} - \frac{y}{2}\right)^{2} \)
Expanded
\[{\left( 1.5 x - 0.5 y \right)}^{2} - {\left( 0.5 x - 1.5 y \right)}^{2} = 2 x^{2} - 2 y^{2}\]
Factored
\[{\left( 1.5 x - 0.5 y \right)}^{2} - {\left( 0.5 x - 1.5 y \right)}^{2} = 2 \left(x - y\right) \left(x + y\right)\]