Atrisiniet (1-lambda)(1-lambda)(2-lambda)+2-lambda

$$( 1 - \lambda ) ( 1 - \lambda ) ( 2 - \lambda ) + 2 - \lambda$$

Izrēķināt

$$\left(\lambda -2\right)\left(-\lambda ^{2}+2\lambda -2\right)$$

Atrisinājuma darbības

Reiziniet 1-\lambda un 1-\lambda , lai iegūtu \left(1-\lambda \right)^{2}.

$$\left(1-\lambda \right)^{2}\left(2-\lambda \right)+2-\lambda$$

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(1-\lambda \right)^{2}.

$$\left(1-2\lambda +\lambda ^{2}\right)\left(2-\lambda \right)+2-\lambda$$

Izmantojiet distributīvo īpašību, katru 1-2\lambda +\lambda ^{2} locekli reizinot ar katru 2-\lambda locekli.

$$2-\lambda -4\lambda +2\lambda ^{2}+2\lambda ^{2}-\lambda ^{3}+2-\lambda$$

Savelciet -\lambda un -4\lambda , lai iegūtu -5\lambda .

$$2-5\lambda +2\lambda ^{2}+2\lambda ^{2}-\lambda ^{3}+2-\lambda$$

Savelciet 2\lambda ^{2} un 2\lambda ^{2}, lai iegūtu 4\lambda ^{2}.

$$2-5\lambda +4\lambda ^{2}-\lambda ^{3}+2-\lambda$$

Saskaitiet 2 un 2, lai iegūtu 4.

$$4-5\lambda +4\lambda ^{2}-\lambda ^{3}-\lambda$$

Savelciet -5\lambda un -\lambda , lai iegūtu -6\lambda .

$$4-6\lambda +4\lambda ^{2}-\lambda ^{3}$$

Paplašināt

$$4-6\lambda +4\lambda ^{2}-\lambda ^{3}$$

Atrisinājuma darbības

Reiziniet 1-\lambda un 1-\lambda , lai iegūtu \left(1-\lambda \right)^{2}.

$$\left(1-\lambda \right)^{2}\left(2-\lambda \right)+2-\lambda$$

Lietojiet Ņūtona binomu \left(a-b\right)^{2}=a^{2}-2ab+b^{2}, lai izvērstu \left(1-\lambda \right)^{2}.

$$\left(1-2\lambda +\lambda ^{2}\right)\left(2-\lambda \right)+2-\lambda$$

Izmantojiet distributīvo īpašību, katru 1-2\lambda +\lambda ^{2} locekli reizinot ar katru 2-\lambda locekli.

$$2-\lambda -4\lambda +2\lambda ^{2}+2\lambda ^{2}-\lambda ^{3}+2-\lambda$$

Savelciet -\lambda un -4\lambda , lai iegūtu -5\lambda .

$$2-5\lambda +2\lambda ^{2}+2\lambda ^{2}-\lambda ^{3}+2-\lambda$$

Savelciet 2\lambda ^{2} un 2\lambda ^{2}, lai iegūtu 4\lambda ^{2}.

$$2-5\lambda +4\lambda ^{2}-\lambda ^{3}+2-\lambda$$

Saskaitiet 2 un 2, lai iegūtu 4.

$$4-5\lambda +4\lambda ^{2}-\lambda ^{3}-\lambda$$

Savelciet -5\lambda un -\lambda , lai iegūtu -6\lambda .

$$4-6\lambda +4\lambda ^{2}-\lambda ^{3}$$