[(x-2)^2]*(x+1) -> (x-2)*(x-2)*(x+1) -> (remember FOIL (first outer inner last)) (x^2 -2*x - 2*x+4 )*(x+1) -> (x^2-4x+4)*(x+1)
then distribute the x+1 to all the terms: x^2*(x+1)-4*x*(x+1)+4*(x+1)
then distribute to each term and add like terms. Try the second problem using these methods to get the hang of it yourself. You can also watch this video (esp prob. 3) on the FOIL method:
http://www.brightstorm.com/d/math/s/algebra/u/polynomials-2/t/multiplying-monomials-andor-binomials-and-foil