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Judge the identity
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Solve the equation
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$ $ TRUE $ $
Judge the identity
$a ^ { 2 } + b ^ { 2 } = \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) ^ { \color{#FF6800}{ 2 } } + 2 a b$
$ $ Expand the binomial expression $ $
$a ^ { 2 } + b ^ { 2 } = \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } + \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } + 2 a b$
$a ^ { 2 } + b ^ { 2 } = a ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } + b ^ { 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b }$
$ $ Eliminate opponent number $ $
$a ^ { 2 } + b ^ { 2 } = a ^ { 2 } + b ^ { 2 }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } }$
$ $ Since the values to calculate for all terms are equal, this expression is an identity $ $
$ $ TRUE $ $
$ $ There are countless solutions $ $
Solve the equation
$a ^ { 2 } + b ^ { 2 } = \left ( \color{#FF6800}{ a } \color{#FF6800}{ - } \color{#FF6800}{ b } \right ) ^ { \color{#FF6800}{ 2 } } + 2 a b$
$ $ Expand the binomial expression $ $
$a ^ { 2 } + b ^ { 2 } = \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } + \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } + 2 a b$
$a ^ { 2 } + b ^ { 2 } = a ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b } + b ^ { 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ a } \color{#FF6800}{ b }$
$ $ Eliminate opponent number $ $
$a ^ { 2 } + b ^ { 2 } = a ^ { 2 } + b ^ { 2 }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ a } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ b } ^ { \color{#FF6800}{ 2 } }$
$ $ Since both sides are the same, this equation is true regardless of the variable $ $
$ $ There are countless solutions $ $
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