Maths with letters!

• 12, 6, 2, 3.14, 22,317, -6, 123Constants(Don’t Change)

• x, y , z , a, b, cVariables(Unknown Numbers)

Order of Operations

• B• O• M• D• A• S

3 X a= 3a

4 X 5 X y= 20y

2 X a X 3 X b= 2 X 3 X a X b= 6ab

a X b= ab

5 X 6y= 30y

2 X 3xy X 5z= (2)(3)(5)xyz= 30xyz

Multiplying 1

Substitution 1If x = 3 and y = 4, find the value of

4x + y4(3) + 412 + 416

xy(3)(4)12

3x – 2y3(3) – 2(4)9 - 81

3xy- 2y3(3)(4) – 2(4)36 – 828

6x – 3y + 56(3) – 3(4) + 518 – 12 + 511

Adding and Subtracting Integers

0 1 2 3 4 5 6-1-2-3-4-5-6

0 1 2 3 4 5 6-1-2-3-4-5-6

0 1 2 3 4 5 6-1-2-3-4-5-6

Adding and Subtracting Integers

Same signs add and keep,Different signs subtract,

Keep the sign of the higher number,Then it’ll be exact,

-3 -4 = -7 4-6 = -2 -7 + 4 = -3-3 + 4 - 2 +5 + 9 – 6= -3 -2 -6 + 4 + 5 +9 = -11 + 18 = 7

Adding Like Terms

• Look for the Like Terms• Rewrite with the Like Terms Together• Add and Subtract the Like Terms

2a + 4xy + 7 – 9xy + 3a – 3 – a

2a + 4xy + 7– 9xy+ 3a – 3– a

4a – 5xy + 4

Adding Like Terms

(i) 3x + 4 + 5x -2= 3x + 5x + 4 -2= 8x + 2

(ii) 3a + 4b –a + 2b + 2a= 3a –a + 2a + 4b + 2b= 4a + 6b

Adding Like Terms3x + 4 + 5x – 23x + 5x + 4 – 28x +2

3a + 4b –a – 7b + 2a3a – a + 2a + 4b – 7b4a – 3b

2ab + c + 5ab + 2c2ab + 5ab + c + 2c7ab + 3c

4xy + 2x + 4x - 8xy – x4xy – 8xy + 2x + 4x – x– 4xy + 5x

Multiplying + -• Like Signs Give Plus

• Unlike Signs Give Minus

3 X 4 = 12

6 X – 2 = – 12

– 2 X – 4 = 8

– 3(3x) = – 9x

– 5 X 3 = – 15

a) 5 X 5 =d) – 4 X – 3 =

b) – 5 X – 2 = e) 3 X – 7 =

c) – 3 X 2 = f) – 4 X – 6 =

g) 3(2x) = h) 3(–2x) = i) –3(–2x)j) – 3(2x) = k) – 3(2x + 6) = l) –3(2x – 6)

– 3(– 4x) = 12x

Removing Brackets4 (3 + 2)

3 (x + 2)

5(2a + 3b)

2(x+4) + 3(2x +6)

2(3x +2y – 4)

– 2(2y – 4)

12 + 820

3x + 6

10a +15b

2x +8 +6x +18

2x +8+6x +188x +26

6x +4y – 8

– 4y + 8

Indices22

= 2 X 2= 4

32

= 3 X 3= 9

23

= 2 X 2 X 2= 8

43

= 4 X 4 X 4 = 64

a2

= a X a

b3

= b X b X b

52

= 5 X 5= 25

54

= 5 X 5 X 5 X 5= 625

y4

= y X y X y X y

y X y= y2

a X a= a2

2a X 3a= 6a2

Removing Bracketsx(x + 2)

2x(x + 4)

3x(2x – 9)

2x(x+4) + 5x(3x – 2)

x2 + 2x

2x2 + 8x

6x2 – 27x

2x2 +8x +15x2 – 10x

2x2 +8x+15x2 – 10x17x2 – 2x

– a(a+3) + 3a(5a – 2)– a2 – 3a +15a2 – 6a

– a2 – 3a+15a2 – 6a14a2 – 9a

b(b – 3) – 3b(– 5b – 2)b2 – 3b +15b2 + 6b

b2 – 3b+15b2 + 6b16b2+ 3b

Substitution 2If x = 3 and y = 4, find the value of

x2

32

3 X 39

2x2 – 2y2(32) – 2(4)2( 3 X 3) – 82 (9) – 8 = 10

6x – 3y + 56(3) – 3(4) + 518 – 12 + 511

y2

42

4 X 416

2x2 – 2y2(32) – 2(4)2( 3 X 3) – 82 (9) – 8 = 10

Removing More Brackets!

x +2

x2 +3x +2x +6x2 +5x +6

(x + 2) (x + 3)(x + 3)(x + 3)

2x – 5

2x2 +6x – 5x –152x2 +x – 15

(2x – 5) (x + 3)(x + 3)(x + 3)

4x + 4

8x2 – 12x + 8x –128x2 – 4x – 12

(4x + 4) (2x – 3)(2x – 3)(2x – 3)

x +2

x2 +3x +xy +2xx2 +3x +6

(x + 2) (x + 3 + y)(x + 3 + y)(x + 3 + y)

+6 +2y+2x +xy +2y

x2 +5x +6+xy +2y

Simplify

• Multiply Out the Brackets• Add and Subtract the Like Terms

2(x+4) + 5(x -2)

2x + 8 + 5x – 10

2x + 8 – 10+ 5x

7x – 2