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Expand the expression
Answer
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Factorize the expression
Answer
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$\left( a+b \right) ^{ 2 } - \left( b-c \right) ^{ 2 }$
$a ^ { 2 } + 2 a b + 2 b c - c ^ { 2 }$
Organize polynomials
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \right ) ^ { \color{#FF6800}{ 2 } } - \left ( b - c \right ) ^ { 2 }$
$ $ Expand the binomial expression $ $
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } + \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } - \left ( b - c \right ) ^ { 2 }$
$a ^ { 2 } + 2 a b + b ^ { 2 } - \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Expand the binomial expression $ $
$a ^ { 2 } + 2 a b + b ^ { 2 } - \left ( \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \right )$
$a ^ { 2 } + 2 a b + b ^ { 2 } \color{#FF6800}{ - } \left ( \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ + } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } } \right )$
$ $ Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses $ $
$a ^ { 2 } + 2 a b + b ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } + \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$ $ Organize the similar terms $ $
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } \color{#FF6800}{ + } \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ c } \color{#FF6800}{ - } \color{#FF6800}{ c } ^ { \color{#FF6800}{ 2 } }$
$a ^ { 2 } + 2 a b + \left ( \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } + 2 b c - c ^ { 2 }$
$ $ Organize the mononomial expression $ $
$a ^ { 2 } + 2 a b + \color{#FF6800}{ 0 } + 2 b c - c ^ { 2 }$
$a ^ { 2 } + 2 a b \color{#FF6800}{ + } \color{#FF6800}{ 0 } + 2 b c - c ^ { 2 }$
$ $ 0 does not change when you add or subtract $ $
$a ^ { 2 } + 2 a b + 2 b c - c ^ { 2 }$
$\left ( a + c \right ) \left ( a + 2 b - c \right )$
Arrange the expression in the form of factorization..
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ b } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ Factorize to use the polynomial formula of sum and difference $ $
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ c } \right )$
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ c } \right )$
$ $ Sort the factors $ $
$\left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ c } \right ) \left ( \color{#FF6800}{ a } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ b } \color{#FF6800}{ - } \color{#FF6800}{ c } \right )$
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