Resolver (1-lambda)(1-lambda)(2-lambda)+2-lambda

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

Avaliar

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

Passos Para a Resolução

Multiplique 1-\lambda e 1-\lambda para obter \left(1-\lambda \right)^{2}.

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

Utilize o teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(1-\lambda \right)^{2}.

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

Aplique a propriedade distributiva ao multiplicar cada termo de 1-2\lambda +\lambda ^{2} por cada termo de 2-\lambda .

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

Combine -\lambda e -4\lambda para obter -5\lambda .

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

Combine 2\lambda ^{2} e 2\lambda ^{2} para obter 4\lambda ^{2}.

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

Some 2 e 2 para obter 4.

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

Combine -5\lambda e -\lambda para obter -6\lambda .

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

Expandir

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

Passos Para a Resolução

Multiplique 1-\lambda e 1-\lambda para obter \left(1-\lambda \right)^{2}.

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

Utilize o teorema binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para expandir \left(1-\lambda \right)^{2}.

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

Aplique a propriedade distributiva ao multiplicar cada termo de 1-2\lambda +\lambda ^{2} por cada termo de 2-\lambda .

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

Combine -\lambda e -4\lambda para obter -5\lambda .

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

Combine 2\lambda ^{2} e 2\lambda ^{2} para obter 4\lambda ^{2}.

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

Some 2 e 2 para obter 4.

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

Combine -5\lambda e -\lambda para obter -6\lambda .

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