1. Algebra topic so far Algebra basics
Simplify expressions by collecting like terms
Directed Numbers
Simplify Expressions by multiplying

2. Simplifying Expressions by multiplying
What is 3 x a equal to?
It means we have three lots of a.
We simplify to 3a
What is 5 x b equal to?
It means we have five lots of b, i.e.
b + b + b + b + b = 5b

3. Simplifying Expressions by multiplying
What is a x a equal to?
Anything multiplied by itself is a square number
So a x a = a2.
What is a x b?
a x b = ab

4. Simplifying Expressions by multiplying
Multiply the numbers first
Then multiply the letters
Put them together
Example
4n x 3m =
12nm

5. Multiplying Expressions
EXAMPLES
Simplify:
(b)
m x t
(c)
2t x 5
(a)
2 x t
= t
= mt
= t 2
(e)
t multiplied by t
(f)
2p x 4p 3
(d)
3y x 2m
= t 2
= p 5
= my 5

6. Simplifying Expressions by multiplying
Examples
5a x -3 =
-9c x 5 =
-4f x -3 =
-2g x 5g =
-6h x -4d =
-15a
-45c
12f
-10g2
24dh

7. Simplifying Expressions by multiplying
-4 × -3k =
-8r × 6w =
-8m × -6m =
4a × -9b =
-6ab × -8 =
-9k × k =
-v × v =
-c × –c =
-t2 × t =
-4b
12k
-48rw
48m2
-36ab
48ab
-9k2
-v2 c2
-t3

8. Title: Simplifying by Multiplying Expressions
2 x a = 2a
Rules and Hints
Do not use a “x” sign or simply remove it 3 x a = 3a
Multiply “numbers” first 3a x 2b = 6__
Remember your negative rules -3 x 2 = -6
Multiply “letters” second a x b = ab
If it’s the same letter add the indices (powers)
Remember a = a1 so a x a = a1 x a1 = a2
Letters go side by side in alphabetical order
2a x 3b x 4c = 24abc
(8) ab2 means a1 x b1 x b1 only the b is squared
(9) (ab) 2 means a1b1 x a1b1 = a 2 b 2 so everything inside is raised by the outside indices (power)
(10) (a3b2)2 when there is a bracket multiply the inside indices by
what’s on the outside so here it Is a6b4
a x a = a2
2a x 2b = 4 ab
a x a x a = a3
3a x 4a = 12 a2
2a b x 2b a = 4
a2b2
a4 x a5 = a9
-a x -bc =
abc 1 1
- a b2 x 2b = -2
ab2 x -2a = -2
a2b2 1
ab3
(ab)2 =
a b x a b
= a2b2
(a2b3)3 =
= a6b9
a2b3 x a2b3 x a2b3
Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide

9. Title: Simplifying by Multiplying Expressions
b2c d3 b2 ab zy 3d
3dc
12t3c
7abc
6ab
20xy
40gh
4abc
3ab
6ab
-2abc
36st
-21abcdef
24dc
Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide

10. Title: Simplifying by Multiplying Expressions
PLENARY
2 x _ = -10ab
3a x _ = 3a3
2b3 x _ = -6a3b4c
-5ab a2
-3a3bc
abc 3
a6 b3 x a2b2 = a8 b5
( __ ) 3 = a3b3c3
(ab2c3) =a3b6c9
(a2b)3 x (ab)2 =
Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide