( m + n )² - ( m - n )² = m² + 2mn + n² - ( m² - 2mn + n² ) = m² + 2mn + n² - m² + 2mn - n² = 4mn.
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( m + n )² - ( m - n )² = m² + 2mn + n² - ( m² - 2mn + n² ) = m² + 2mn + n² - m² + 2mn - n² = 4mn.