Let us assume that:

E = 2 ( a-3) + 4b - 2( a - b - 3 ) + 5

First we will expand between brackets by multiplying all terms by 2:

==> E = 2*a + 2*-3 + 4b - 2*a - 2*-b - 2*-3 + 5

==>...

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Let us assume that:

E = 2 ( a-3) + 4b - 2( a - b - 3 ) + 5

First we will expand between brackets by multiplying all terms by 2:

==> E = 2*a + 2*-3 + 4b - 2*a - 2*-b - 2*-3 + 5

==> E = 2a - 6 + 4b - 2a + 2b + 6 + 5

Now we will combine like terms:

==> E = 2a - 2a + 4b + 2b - 6 + 6 + 5

Now we will eliminate similar terms :

We note that 2a - 2a = 0

Also, we have 6- 6 = 0

==> E = 0 + 6b + 0 + 5

==> E = 6b + 5

Then after simplifying , the expression is:

**2 ( a-3) + 4b - 2( a - b - 3 ) + 5 = 6b + 5**