$\left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } + \left ( x - y \right ) \left ( x + y \right )$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } + \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } + \left ( x - y \right ) \left ( x + y \right )$
$x ^ { 2 } + 2 x y + y ^ { 2 } + \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ y } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ y } \right )$
$ $ Organize the expression with the distributive law $ $
$x ^ { 2 } + 2 x y + y ^ { 2 } + \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the similar terms $ $
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ y } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + 2 x y + \left ( 1 - 1 \right ) y ^ { 2 }$
$ $ Arrange the constant term $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + 2 x y + \left ( 1 - 1 \right ) y ^ { 2 }$
$2 x ^ { 2 } + 2 x y + \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the mononomial expression $ $
$2 x ^ { 2 } + 2 x y + \color{#FF6800}{ 0 }$
$2 x ^ { 2 } + 2 x y \color{#FF6800}{ + } \color{#FF6800}{ 0 }$
$ $ 0 does not change when you add or subtract $ $
$2 x ^ { 2 } + 2 x y$