ax+a^2x+aby+by-(ax+by)^2
You asked:
Evaluate the expression: \(a x + {a}^{2} x + a b y + b y - {\left( a x + b y \right)}^{2}\)
MathBot Answer:
Evaluated
\(\displaystyle a x + {a}^{2} x + a b y + b y - {\left( a x + b y \right)}^{2} = a^{2} x + a b y + a x + b y - \left(a x + b y\right)^{2} \)
Expanded
\[a x + {a}^{2} x + a b y + b y - {\left( a x + b y \right)}^{2} = - a^{2} x^{2} + a^{2} x - 2 a b x y + a b y + a x - b^{2} y^{2} + b y\]
Factored
\[a x + {a}^{2} x + a b y + b y - {\left( a x + b y \right)}^{2} = - \left(a x + b y\right) \left(a x - a + b y - 1\right)\]