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**

This problem requires the distributive property

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

Since there are two variables distribute but use caution and use PEMDAS

2a - 6 + 4b - 2a +2b +6 +5

Then combine like terms and simplify

2a-2a +2b+4b -6+6+5

6b+5

2(a -3) + 4b - 2(a -9-6b -3) + 5

(2a-2a) l (4b+2b) l (-6 +6+5)

0 + 6b +5

6b+5

2(a -3) + 4b - 2(a -9-6b -3) + 5

distribute the numbers

2a - 6 + 4b - 2a + 2b + 6 +5

combiine like terms

(2a-2a) l (4b+2b) l (-6 +6+5)

0 + 6b +5

the answer is

6b+5

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

First apply distributive property wherever you can:

**2a - 6** + 4b **- 2a + 2b+ 6** + 5

Then combine like terms:

2a - 2a + 4b + 2b - 6 + 6 + 5

6b + 5

Let us assume X = 2(a -3) + 4b - 2(a -b -3) + 5

or, X = 2a - 6 + 4b -2a -2*(-b) -2*(-3) + 5 [we have opened the bracket according to the BODMAS or PEDMAS rule]

or, X = 2a - 2a + 4b+2b +6 -6 +5 [grouped the like terms NOTE: the negative b has become positive since (-*-) results in a +]

Now we will eliminate similar terms :

We see that 2a - 2a = 0

Also, we have 6- 6 = 0

or, X = 0 + 6b + 0 + 5

or, **X = 6b + 5 [Ans.]**

** **Therefore the simplified expression is:

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