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}] $(\because \mathrm{xy}=\mathrm{yx})$
= xy − [yz − zx + 3y - xz - zy]
= xy − [− 2zx + 3y ] $(\because \mathrm{yz}=\mathrm{zy},\mathrm{zx}=\mathrm{xz})$
= xy + 2zx − 3y