${x}^{2}+2x+1-{\left( x-2 \right)}^{2}$
Use ${\left( a-b \right)}^{2}={a}^{2}-2ab+{b}^{2}$ to expand the expression${x}^{2}+2x+1-\left( {x}^{2}-4x+4 \right)$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses${x}^{2}+2x+1-{x}^{2}+4x-4$
Since two opposites add up to $0$, remove them from the expression$2x+1+4x-4$
Collect like terms$6x+1-4$
Calculate the difference$6x-3$