Try to explain that the algebraic formula (x + 1) (x + 2) (x + 3) (x + 4) + 1 is a complete square formula

Try to explain that the algebraic formula (x + 1) (x + 2) (x + 3) (x + 4) + 1 is a complete square formula

(x+1)(x+2)(x+3)(x+4)+1
=(x+1)(x+4)(x+2)(x+3)+1
=(x^2+5x+4)(x^2+5x+6)+1
=(x^2+5x)^2+10(x^2++5x)+25
=(x^2+5x+5)^2