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Question
Simplify:
xy − [yz − zx − {yx − (3y − xz) − (xy − zy)}]
Solution
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
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