Two exercises of common factor extraction in mathematics of grade one in junior high school 1. Using factorization to simplify polynomial 1 + X + X (1 + x) + X (1 + x) ^ 2 + +x(1+x)^2009. 2. Please explain why 13 ^ 2010-2 * 13 ^ 2009 + 5 * 13 ^ 2008 is an integral multiple of 37 I don't have much time to do a lot of homework

Two exercises of common factor extraction in mathematics of grade one in junior high school 1. Using factorization to simplify polynomial 1 + X + X (1 + x) + X (1 + x) ^ 2 + +x(1+x)^2009. 2. Please explain why 13 ^ 2010-2 * 13 ^ 2009 + 5 * 13 ^ 2008 is an integral multiple of 37 I don't have much time to do a lot of homework

1.1+x+x(1+x)+x(1+x)^2+… +x(1+x)^2009=(1+x)+x(1+x)+x(1+x)^2+...+x(1+x)^2009=(1+x)(1+x)+x(1+x)^2+...+x(1+x)^2009=(1+x)^2+x(1+x)^2+...+x(1+x)^2009=(1+x)(1+x)^2+...+x(1+x)^2009=(1+x)^3+...+x(1+x)^2009=(1+...