Solve (lambda-1)^2(lambda-2)

$$( \lambda - 1 ) ^ { 2 } ( \lambda - 2 )$$

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply \lambda ^{2}-2\lambda +1 by \lambda -2 and combine like terms.

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply \lambda ^{2}-2\lambda +1 by \lambda -2 and combine like terms.

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