(a-b+c) is equal to
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a-(b+c) this is the answer for your question.
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a(b+c)=ab+ac ; the right hand side is (a+b)c=ac+bc
These two are equal if and only if ab=bc because you can cancel the common summand ac
In the standard number sets (natural, integer, rational, real, or complex numbers) this is only satisfied for b=0 or a=c
This suggests a counterexample that shows the identity is not valid: choose a=1, b=2 and c=3 (so a≠c and b≠0. Then
a(b+c)=1⋅(2+3)=5
(a+b)c=(1+2)⋅3=9
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