Solve (1-lambda)(1-lambda)(2-lambda)+2-lambda

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

Evaluate

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

Solution Steps

Multiply 1-\lambda and 1-\lambda to get \left(1-\lambda \right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-\lambda \right)^{2}.

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

Apply the distributive property by multiplying each term of 1-2\lambda +\lambda ^{2} by each term of 2-\lambda .

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

Combine -\lambda and -4\lambda to get -5\lambda .

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

Combine 2\lambda ^{2} and 2\lambda ^{2} to get 4\lambda ^{2}.

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

Add 2 and 2 to get 4.

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

Combine -5\lambda and -\lambda to get -6\lambda .

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

Expand

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

Solution Steps

Multiply 1-\lambda and 1-\lambda to get \left(1-\lambda \right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-\lambda \right)^{2}.

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

Apply the distributive property by multiplying each term of 1-2\lambda +\lambda ^{2} by each term of 2-\lambda .

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

Combine -\lambda and -4\lambda to get -5\lambda .

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

Combine 2\lambda ^{2} and 2\lambda ^{2} to get 4\lambda ^{2}.

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

Add 2 and 2 to get 4.

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

Combine -5\lambda and -\lambda to get -6\lambda .

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