expand the brackets and simplify these?

a(b+c) = ab + ac

So, 3(4a+5) + 2(3a+4) = 12a + 15 + 6a + 8 = 18a + 23

Get the idea?

1a
3(4a+5)+2(3a+4)
12a +15 + 6a +8
12a + 6a +15 + 8
18a +23

1b
5(4b+3)+3(2b+1)
20b+15 +6b+3
20b +6b + 15+3
26b =18

1c
2(3+6c)+4(5+7c)
6+12c +20+28c
12c+28c +6 +20
40c+26

Answers:
1.A.

3(4a+5)+2(3a+4)=12a+15+6a+8
=18a+23.

1.B.

5(4b+3)+3(2b+1)=20b+15+6b+3
=26b+18.

1.C.

2(3+6c)+4(5+7c)=6+12c+20+28c
=40c+26.

2.A.

2(4x+5)+3(5x-2)=8x+10+15x-6
=23x+4.


2.B.

4(3y+2)+5(3y-2)=12y+8+15y-10
=27y-2.

2.C.

3(4+7z)+2(3-5z)=12+21z+6-10z
=11z+18.

How to solve:
Consider example 2.A.
Multiply the number outside each bracket with all the terms inside the bracket. So multiply 2 by 4x, and multiply 2 by 5, to give 8x and 10 respectively. Similarly, multiple 3 by 5x and 3 by -2 to give 15x and -6 respectively. Now add/subtract the similar terms i.e. those terms having the same variable. So add 8x & 15x, and subtract 6 from 10.

Expanding the brackets means writing it in its simplest form.
Or you can simply say that you have to remove all the brackets.
Here yoy have to use the BODMAS formula
B=Brackets
O=Off
D=Division
M=Multiplication
A=Addition
S=Subtraction
These all are arranged priority wise.

1.A.
=3(4a+5)+2(3a+4)
={(3*4a)+(3*5)} + {(2*3a)+(2*4)}
=12a+15+6a+24
=18a+39

Similarly you can do the rest of the questions.

These are all worked the same way. Let me do the first one for you:
1.A.
3(4a+5) + 2(3a+4) =
12a + 15 + 6a + 8 =
18a + 23

Work the rest of them the same way.

1 A)
3(4a + 5) + 2(3a + 4)
= 3*4a + 3*5 + 2*3a + 2*4
= 12a + 15 + 6a + 8
= 12a + 6a + 15 + 8
= 18a + 23

1 B)
5(4b + 3) + 3(2b + 1)
= 5*4b + 5*3 + 3*2b + 3*1
= 20b + 15 + 6b + 3
= 20b + 6b + 15 + 3
= 26b + 18
= 2(13b + 9)

1 C)
2(3 + 6c) + 4(5 + 7c)
= 2*3 + 2*6c + 4*5 + 4*7c
= 6 + 12c + 20 + 28c
= 12c + 28c + 6 + 20
= 40c + 26
= 2(20c + 13)

----------------

2 A)
2(4x + 5) + 3(5x - 2)
= 8x + 10 + 15x - 6
= 8x + 15x + 10 - 6
= 23x + 4

2 B)
4(3y + 2) + 5(3y - 2)
= 12y + 8 + 15y - 10
= 12y + 15y + 8 - 10
= 27y - 2

2 C)
3(4 + 7z) + 2(3 - 5z)
= 12 + 21z + 6 - 10z
= 21z - 10z + 12 + 6
= 11z + 18

This is back to the old 'bodmas' - brackets, of, division, multiplication, addition, subtraction - you do the operations in that order.
So, if we take the first one:
3(4a+5) +2(3a+4) this expands to
3x4a+ 3x5 +2x3a+2x4 (using x for multiplication), or
12a+15 + 6a+8 which reduces to
18a+23

The others are the same but just watch out for the signs. Remember
a) minus times plus equals minus and
b) minus times minus equals plus

1 a) 12a + 15 + 6a + 8 = 18a + 23
b) 20b + 15 + 6b + 3 = 26b + 18 = 2(13b + 9)
c) 6 + 12c + 20 +28c = 40c + 26 = 2(20c + 13)

2 a) 4x + 10 + 15x - 6 = 19x + 4
b) 12y + 8 + 15y - 10 = 17y - 2
c) 12 + 21z + 6 -10z = 11z + 18

Just multiply the stuff outside the brackets with every term inside the brackets and then add similar terms up together. Beware that negative times positive is negative and negative times negative is positive!

Just to wrap things up...don't do what this 'Peter' did...http://www.comedymail.co.uk/getPicture.asp?Filename=content/image010.jpg

1A
=3*4a + 3*5 + 2*3a + 2*4
=12a + 15 + 6a + 8
=18a + 23
1B
5*4b + 5*3 + 3*2b + 3*1

get the picture?

Let me think about this
Ok, i got it
1A) 3(4a+5)+2(3a+4) = 18a+23

because you multiply what is inside the bracket by what is outside the brackets. So first we would do 3 x 4a, which equals 12a. Then we would do 3 x 5, which equals 15.
Then multiply out the second bracket. 2 x 3a, which equals 6a, then 2 x 4, which equals 8.
Then you add all four answers together because the plus sign is what is used in the question - so you get:
12a + 15 + 6a + 8
And to simplify you would add both of the ones containing 'a' - which would be 12a + 6a, which equals 18a.
Then add the other one that don't contain 'a' - 15 + 8, which equals 23.
Then you add the 18a and 23 so you get
18a + 23 as the final answer.
You cannot add these two together because they have not got common terms. (A common term means they both have the same letter after them. E.g 'a' or 'b' or any other letter)

You can work out the rest of the questions in the same way.
For question 2 where some of them have a minus sign, instead of adding, just take it away.

2A) 2(4x+5)+3(5x-2)
= 8x + 10 + 15x -6
= 23x + 4

Instead of doing 10 + 6 , you must do 10 - 6 because in the sum the 6 has a minus sign infront of it.

I hope this helps
Good Luck
xxx