Calculate: (x+1)^2-(x-2)^2

Expression: ${\left( x+1 \right)}^{2}-{\left( x-2 \right)}^{2}$

Use ${\left( a+b \right)}^{2}={a}^{2}+2ab+{b}^{2}$ to expand the expression

${x}^{2}+2x+1-{\left( x-2 \right)}^{2}$

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

$6x-3$