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SIMPLIFYING ALGEBRAIC EXPRESSIONS. ADDING LIKE TERMS. MULTIPLYING LIKE TERMS. SIMPLIFYING EXPRESSIONS. REPLACING LETTERS WITH NUMBERS TO GET A VALUE FOR AN EXPRESSION. USING FORMULAS. REMOVING BRACKETS. ADDING LIKE TERMS. 3 + 3 + 3 + 3. Can be written in the shorter form.

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simplifying algebraic expressions
SIMPLIFYING ALGEBRAIC EXPRESSIONS
  • ADDING LIKE TERMS
  • MULTIPLYING LIKE TERMS
  • SIMPLIFYING EXPRESSIONS
  • REPLACING LETTERS WITH NUMBERS TO GET A VALUE FOR AN EXPRESSION
  • USING FORMULAS
  • REMOVING BRACKETS
adding like terms
ADDING LIKE TERMS

3 + 3 + 3 + 3

Can be written in the shorter form

Meaning that we have 4 bundles of 3’s

4 X 3

This gives the VALUE

12

Can be written in the shorter form

a + a + a + a

We cannot give a value for 4a until we are given a value for a

4a

slide3

If a = 7

Then by replacing a with 7

4a

= 4 x(7)

= 28

So a value for the expression 4a when a = 7 is

28

slide4

Some examples

Simplify the following expressions

Combine all the a’s together to get one term

3a + 2a

= a+a+a + a+a

= 5a

5b – 2b

= b + b + b + b + b

- b + b

Take 2 b’s away from the 5 b’s

= 3b

simplifying expressions with numbers and different letters
Simplifying expressions with numbers and different letters

Simplify 3a + 2b + 5a + 3b + 7

WE can only add or subtract like terms to each other

+

2b + 3b

7

3a + 5a

+

5b

8a

+

7

+

8a + 5b +7

multiplying like terms
Multiplying like terms

Can be written in the shorter form

2 X 2 X 2 X 2 X2

This means that 2 is multiplied by itself 5 times

25

This gives a value

32

a X a X a X a X a

Can be written in the shorter form

We cannot get a value for a5 until we are given a value for a

a5

slide7

If a = 7 then

a5

= 75

=16807

So a value for the expression a5 when a = 7 is 16807

slide8

Some examples

Simplify the following expressions

3a x a

= 3 x a x a x a x a

We now have 3 times a multiplied by itself 4 times

= 3a4

3b x 2b

= 3 x 2 x b x b

Multiply the numbers together and multiply the letters together

= 6 x b2

Write product without multiplication sign

= 6 b2

slide9

Examples with numbers and letters

  • 3b2 X 4b3

3X4

X

b2X b3

12

X

bXb X bXbXb

b2X b3 = b2+3 =b5

X

12

b5

Add the powers

Multiply the numbers together

slide10

Simplify

REMEMBER

  • r = r1

4r x 6s x r2 x s3

r x r2

= 4 x 6

s x s3

x

x

Multiply similar letters together by adding the powers

Multiply the numbers together

s1+3

24

x

r1+2

x

When we multiply letters and numbers first put the numbers next the letters in alphabetical order and we do not need the X sign

=24 r3s4

order of operations
Order of operations

=

Not 21

5 + 2 x 3

11

In mathematics we have rules

Multiplication or division is calculated before addition or subtraction

Is simplified to

2 x a + 5

2a + 5

Is simplified to

6 – 2 x b

6-2b

have you got it yet
Have you got it yet ?

Simplify the following

5a

8 . 3m + 2m + 7

5m+ 7

1. 2a + 3a

9. 6j – 3j + j

5a + 9b

4j

2. 3a + 4b + 2a + 5b

3. b x b x b x b

b4

10. 3s x 4s x 6

72b2

4. b x b x c x c x c

11. 3 x s + 7

3s+7

b2c3

20b5

6+3d

5. 4b2 x 5b3

12. 6 + 3 x d

13 . 10n – 2 x 3n

4n

12bc

6. 3c x 4b

.

5c4

14. 8b – 3 x b2

8b – 3 b2

7. 2 c 4 + 3c4

finding values for expressions
Finding values for expressions

Find a value for the expression 3b when b =7

3 x (7)

3b =

= 21

21 is the value of the expression

Take out b and replace it with 7

Put 7 inside a bracket

slide14

Find a value for the expression 3c + b when c = 2 and b = 5

3c + b

Replace c with 2 and b with 5

= 3 x (2) + ( 5)

= 6 + 5

= 11

11 is the value of the expression

slide15

Find a value for the expressions a) pq b) 2p + q c) 5pq +2p d) q2 -p2 when e) 3 ( p + 2q ) f) ( p + q ) 2 when p = 3 and q = 7

a) pq

b) 2p + q

c) 3pq + 2p

= 3 x ( 3 ) x ( 7 ) + 2 x ( 3 )

= (3) x (7)

= 2 x ( 3) + ( 7 )

= 63 + 6

= 6 + 7

= 21

= 13

= 69

q2 -p2

d)

e) 3 ( p + 2q )

f) ( q - p ) 2

= (7)2 - (3)2

= 3 ( (7) + 2x(3) )

= ( (7) – (3) ) 2

= 49 - 9

= 3( 7 + 6)

= ( 4 ) 2

= 40

39

= 3 x 13 =

= 16