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Expand the expression
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$a ^ { 2 } - 7 a + 13 b - 20$
Organize polynomials
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) - \left ( 2 a + 1 \right ) \left ( 2 - b \right )$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ a } + \color{#FF6800}{ 12 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 18 } - \left ( 2 a + 1 \right ) \left ( 2 - b \right )$
$a ^ { 2 } - 2 a b - 3 a + 12 b - 18 \color{#FF6800}{ - } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( 2 - b \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$a ^ { 2 } - 2 a b - 3 a + 12 b - 18 + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( 2 - b \right )$
$a ^ { 2 } - 2 a b - 3 a + 12 b - 18 + \left ( - 2 a - 1 \right ) \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ b } \right )$
$ $ Sort the polynomial expressions in descending order $ $
$a ^ { 2 } - 2 a b - 3 a + 12 b - 18 + \left ( - 2 a - 1 \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$a ^ { 2 } - 2 a b - 3 a + 12 b - 18 + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right )$
$ $ Organize the expression with the distributive law $ $
$a ^ { 2 } - 2 a b - 3 a + 12 b - 18 + \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ a } + \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 12 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 18 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ 2 }$
$ $ Organize the similar terms $ $
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ a } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ b } \color{#FF6800}{ + } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 18 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$a ^ { 2 } + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) \color{#FF6800}{ a } \color{#FF6800}{ b } + \left ( - 3 - 4 \right ) a + \left ( 12 + 1 \right ) b + \left ( - 18 - 2 \right )$
$ $ Organize the mononomial expression $ $
$a ^ { 2 } + \color{#FF6800}{ 0 } + \left ( - 3 - 4 \right ) a + \left ( 12 + 1 \right ) b + \left ( - 18 - 2 \right )$
$a ^ { 2 } + 0 + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \color{#FF6800}{ a } + \left ( 12 + 1 \right ) b + \left ( - 18 - 2 \right )$
$ $ Arrange the constant term $ $
$a ^ { 2 } + 0 \color{#FF6800}{ - } \color{#FF6800}{ 7 } \color{#FF6800}{ a } + \left ( 12 + 1 \right ) b + \left ( - 18 - 2 \right )$
$a ^ { 2 } + 0 - 7 a + \left ( \color{#FF6800}{ 12 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ b } + \left ( - 18 - 2 \right )$
$ $ Arrange the constant term $ $
$a ^ { 2 } + 0 - 7 a + \color{#FF6800}{ 13 } \color{#FF6800}{ b } + \left ( - 18 - 2 \right )$
$a ^ { 2 } + 0 - 7 a + 13 b + \left ( \color{#FF6800}{ - } \color{#FF6800}{ 18 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right )$
$ $ Arrange the constant term $ $
$a ^ { 2 } + 0 - 7 a + 13 b \color{#FF6800}{ - } \color{#FF6800}{ 20 }$
$a ^ { 2 } \color{#FF6800}{ + } \color{#FF6800}{ 0 } - 7 a + 13 b - 20$
$ $ 0 does not change when you add or subtract $ $
$a ^ { 2 } - 7 a + 13 b - 20$
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