multiplying parentheses with more variables than (a b) * (c d)

Question

I want to solve $$ (1 - 2\lambda + \lambda^2)(1 - \lambda) + 2 - 3(1 - \lambda) = 0 $$ Eventually I would probably want to factor the polynomial, but I don't know how to multiply the parentheses of the polynomial's first part.

Answer 1

$$(a+b+c)(d+e)=a(d+e)+b(d+e)+c(d+e)$$

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Note that $1-2\lambda +\lambda^2=(1-\lambda)^2$ and set $1-\lambda=X$ to get $$X^3-3X+2=0$$ Now it should be easy to find a solution $X=1$.