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Expand the expression
Answer
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Factorize the expression
Answer
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$a ^{ 2 } \left( b-c \right) +b ^{ 2 } \left( c-a \right) +c ^{ 2 } \left( a-b \right)$
$a ^ { 2 } b - a ^ { 2 } c - a b ^ { 2 } + a c ^ { 2 } + b ^ { 2 } c - b c ^ { 2 }$
Organize polynomials
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) + b ^ { 2 } \left ( c - a \right ) + c ^ { 2 } \left ( a - b \right )$
$ $ Organize the expression with the distributive law $ $
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } + b ^ { 2 } \left ( c - a \right ) + c ^ { 2 } \left ( a - b \right )$
$a ^ { 2 } b - a ^ { 2 } c + b ^ { 2 } \left ( \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ a } \right ) + c ^ { 2 } \left ( a - b \right )$
$ $ Sort the polynomial expressions in descending order $ $
$a ^ { 2 } b - a ^ { 2 } c + b ^ { 2 } \left ( \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ c } \right ) + c ^ { 2 } \left ( a - b \right )$
$a ^ { 2 } b - a ^ { 2 } c + \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ c } \right ) + c ^ { 2 } \left ( a - b \right )$
$ $ Organize the expression with the distributive law $ $
$a ^ { 2 } b - a ^ { 2 } c \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } + c ^ { 2 } \left ( a - b \right )$
$a ^ { 2 } b - a ^ { 2 } c - a b ^ { 2 } + b ^ { 2 } c + \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right )$
$ $ Organize the expression with the distributive law $ $
$a ^ { 2 } b - a ^ { 2 } c - a b ^ { 2 } + b ^ { 2 } c + \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$ $ Sort the polynomial expressions in descending order $ $
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$\left ( a - b \right ) \left ( a - c \right ) \left ( b - c \right )$
Arrange the expression in the form of factorization..
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ a } \right ) \color{#FF6800}{ + } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right )$
$ $ Expand the expression $ $
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ a } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ a } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ b } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$ $ Do factorization $ $
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right )$
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