The second line should be
= − λ [ − λ ( λ 2 − λ k 4 + 1 − k 3 ) + k 2 ] − [ − 2 ( λ 2 − λ k 4 + 1 − k 3 ) − k 1 − 1 ] {\displaystyle =-\lambda \left[-\lambda \left(\lambda ^{2}-\lambda k_{4}+1-k_{3}\right)+k_{2}\right]-\left[-2\left(\lambda ^{2}-\lambda k_{4}+1-k_{3}\right)-k_{1}-1\right]}
The third line should be:
= λ 4 − k 4 λ 3 + ( 3 − k 3 ) λ 2 − ( 2 k 4 + k 2 ) λ + ( 1 − k 1 − 2 k 3 ) = 0. {\displaystyle =\lambda ^{4}-k_{4}\lambda ^{3}+\left(3-k_{3}\right)\lambda ^{2}-\left(2k_{4}+k_{2}\right)\lambda +\left(1-k_{1}-2k_{3}\right)=0.}