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Expand the expression
Answer
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Factorize the expression
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$\left( 3x+1 \right) \left( x-2 \right) - \left( 2x-1 \right) ^{ 2 }$
$- x ^ { 2 } - x - 3$
Organize polynomials
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) - \left ( 2 x - 1 \right ) ^ { 2 }$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } - \left ( 2 x - 1 \right ) ^ { 2 }$
$3 x ^ { 2 } - 5 x - 2 - \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the binomial expression $ $
$3 x ^ { 2 } - 5 x - 2 - \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$3 x ^ { 2 } - 5 x - 2 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$3 x ^ { 2 } - 5 x - 2 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 }$
$ $ Organize the similar terms $ $
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \left ( - 5 + 4 \right ) x + \left ( - 2 - 1 \right )$
$ $ Organize the mononomial expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + \left ( - 5 + 4 \right ) x + \left ( - 2 - 1 \right )$
$- x ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ x } + \left ( - 2 - 1 \right )$
$ $ Organize the mononomial expression $ $
$- x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ x } + \left ( - 2 - 1 \right )$
$- x ^ { 2 } - x + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right )$
$ $ Arrange the constant term $ $
$- x ^ { 2 } - x \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$- \left ( x ^ { 2 } + x + 3 \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$\color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Bind the expressions with the common factor $ - 1$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right )$
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