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Expand the expression
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Factorize the expression
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$2 \left( p+q \right) ^{ 2 } - \left( p+q \right) p-6p ^{ 2 }$
$- 5 p ^ { 2 } + 3 p q + 2 q ^ { 2 }$
Organize polynomials
$2 \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( p + q \right ) p - 6 p ^ { 2 }$
$ $ Expand the binomial expression $ $
$2 \left ( \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \right ) - \left ( p + q \right ) p - 6 p ^ { 2 }$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \right ) - \left ( p + q \right ) p - 6 p ^ { 2 }$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 4 } \color{#FF6800}{ p } \color{#FF6800}{ q } + \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } - \left ( p + q \right ) p - 6 p ^ { 2 }$
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) p - 6 p ^ { 2 }$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ - } \color{#FF6800}{ q } \right ) p - 6 p ^ { 2 }$
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ - } \color{#FF6800}{ q } \right ) \color{#FF6800}{ p } - 6 p ^ { 2 }$
$ $ Organize the expression with the distributive law $ $
$2 p ^ { 2 } + 4 p q + 2 q ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ q } - 6 p ^ { 2 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the similar terms $ $
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } }$
$\left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } + \left ( 4 - 1 \right ) p q + 2 q ^ { 2 }$
$ $ Arrange the constant term $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } + \left ( 4 - 1 \right ) p q + 2 q ^ { 2 }$
$- 5 p ^ { 2 } + \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ p } \color{#FF6800}{ q } + 2 q ^ { 2 }$
$ $ Arrange the constant term $ $
$- 5 p ^ { 2 } + \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } + 2 q ^ { 2 }$
$- \left ( 5 p ^ { 2 } - 3 p q - 2 q ^ { 2 } \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ p } \color{#FF6800}{ + } \color{#FF6800}{ q } \right ) \color{#FF6800}{ p } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } }$
$ $ Bind the expressions with the common factor $ - 1$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ 5 } \color{#FF6800}{ p } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ p } \color{#FF6800}{ q } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ q } ^ { \color{#FF6800}{ 2 } } \right )$
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