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Judge the identity
Solve the equation
$a ^{ 2 } +b ^{ 2 } = \left( a-b \right) ^{ 2 } +2ab$
 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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