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Formula
Expand the expression
$3 \left( x-1 \right) ^{ 2 } - \left( 2x+1 \right) \left( x-3 \right)$
$x ^ { 2 } - x + 6$
Organize polynomials
$3 \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( 2 x + 1 \right ) \left ( x - 3 \right )$
 Expand the binomial expression 
$3 \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - \left ( 2 x + 1 \right ) \left ( x - 3 \right )$
$\color{#FF6800}{ 3 } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) - \left ( 2 x + 1 \right ) \left ( x - 3 \right )$
 Organize the expression with the distributive law 
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } + \color{#FF6800}{ 3 } - \left ( 2 x + 1 \right ) \left ( x - 3 \right )$
$3 x ^ { 2 } - 6 x + 3 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( x - 3 \right )$
 Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses 
$3 x ^ { 2 } - 6 x + 3 + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( x - 3 \right )$
$3 x ^ { 2 } - 6 x + 3 + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right )$
 Organize the expression with the distributive law 
$3 x ^ { 2 } - 6 x + 3 \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 5 } \color{#FF6800}{ x } + \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 }$
 Organize the similar terms 
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \left ( - 6 + 5 \right ) x + \left ( 3 + 3 \right )$
 Organize the mononomial expression 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \left ( - 6 + 5 \right ) x + \left ( 3 + 3 \right )$
$x ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \right ) \color{#FF6800}{ x } + \left ( 3 + 3 \right )$
 Organize the mononomial expression 
$x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } + \left ( 3 + 3 \right )$
$x ^ { 2 } - x + \left ( \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
 Arrange the constant term 
$x ^ { 2 } - x + \color{#FF6800}{ 6 }$
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