It is proved that the value of X (x + 1) (x + 2) (x + 3) + 1 is a complete square expression Try to be quick

It is proved that the value of X (x + 1) (x + 2) (x + 3) + 1 is a complete square expression Try to be quick

Because there is x (x + 1) (x + 2) (x + 3) + 1, the treatment of this polynomial is generally transposition, try to appear the same number of terms, can be replaced by X (x + 3) (x + 1) (x + 2) + 1, after expansion, we get (x ^ 2 + 3x) (x ^ 2 + 3x + 2) + 1, continue to get (x ^ 2 + 3x) ^ 2 + 2 (x ^ 2 + 3x) + 1 = (x ^ 2 + 3x + 1) ^ 2, that is the complete square