# Can any one explain the language L = {w: w = uu, u in La (1 * 01 *)}

Consider, as a simpler case, $$A = {a, b }$$ and $$L = {w | w = uu, u in A }$$. Then, $$L = {aa, bb }$$.
Instead, if we apply your simplification and write $$The & # 39; = AA$$ then, we have $$The & # 39; = {aa, ab, ba, bb }$$ which is a bigger language, since we have forgotten that both $$u$$& # 39; sin $$w = uu$$ must be the even word.
Keep this in mind, your language of origin $$L$$ seems to be $${1 ^ n01 ^ m1 ^ n01 ^ m | n, m leq 0 }$$