Question

Simplify:

xy − [yz − zx − {yx − (3y − xz) − (xy − zy)}]

Answer 1

xy − [yz − zx − {yx − (3y − xz) − (xy − zy)}]

We will first remove the innermost grouping symbol ( ), followed by { } and then [ ].

∴ xy − [yz − zx − {yx − (3y − xz) − (xy − zy)}]

= xy − [yz − zx − {yx − 3y + xz − xy + zy}]

= xy − [yz − zx − {− 3y + xz + zy}]  (∵ xy = yx) (∵ xy = yx)

= xy − [yz − zx + 3y - xz - zy] 

= xy − [− 2zx + 3y] (∵ yz = zy, zx = xz) (∵  yz = zy, zx = xz)

= xy + 2zx − 3y