one more than the product of one more than a number with one less than the same number

Answer 1

one more than a number = ( x + 1 )

one less than the same number =

( x - 1 )

one more than the product of one more than a number with one less than the same number =

( x + 1 ) ( x - 1 ) + 1 =

x • x + x • 1 - 1 • x - 1 • 1 + 1 =

x² + x - x - 1 + 1 = x²