Simplify: ( 7/2+5/6 )^2 - ( 7/2-5/6 )^2

Answer 1

7 / 2 = ( 7 / 2 ) * ( 3 / 3 ) = 21 / 6

( 7 / 2 + 5 / 6 ) ^ 2 - ( 7 / 2 - 5 / 6 ) ^ 2 =

( 21 / 6 + 5 / 6 ) ^ 2 - ( 21 / 6 - 5 / 6 ) ^ 2 =

( 26 / 6 ) ^ 2 - ( 16 / 6 ) ^ 2 =

676 / 36 - 256 / 36 =

( 676 - 256 ) / 36 =

420 / 36 =

( 12 * 35 ) / ( 12 * 3 ) = 35 / 3

Answer 2

Or, since it is the difference of two squares,

(7/2+5/6)^2 - (7/2-5/6)^2
= (7/2+5/6 + 7/2-5/6)(7/2+5/6 - 7/2-5/6)
= (7)(5/3)
= 35/3