4r(-p+q+r)-3p(p+q)-2q(p-q+r)
You asked:
Evaluate the expression: \(4 \cdot r \cdot \left(-p + q + r\right) - 3 \cdot p \cdot \left(p + q\right) - 2 \cdot q \cdot \left(p - q + r\right)\)
MathBot Answer:
Evaluated
\(\displaystyle 4 \cdot r \cdot \left(-p + q + r\right) - 3 \cdot p \cdot \left(p + q\right) - 2 \cdot q \cdot \left(p - q + r\right) = - 3 p \left(p + q\right) - 2 q \left(p - q + r\right) + 4 r \left(- p + q + r\right) \)
Expanded
\[4 \cdot r \cdot \left(-p + q + r\right) - 3 \cdot p \cdot \left(p + q\right) - 2 \cdot q \cdot \left(p - q + r\right) = - 3 p^{2} - 5 p q - 4 p r + 2 q^{2} + 2 q r + 4 r^{2}\]
Factored
\[4 \cdot r \cdot \left(-p + q + r\right) - 3 \cdot p \cdot \left(p + q\right) - 2 \cdot q \cdot \left(p - q + r\right) = - 3 p^{2} - 5 p q - 4 p r + 2 q^{2} + 2 q r + 4 r^{2}\]