Algebra

Algebra

Expanding Brackets
1. 6(x+y)
  1. =6x+6y
2. https://www.youtube.com/watch?v=-mVG_6745B8
3. 2(x+3)
  1. =2x+6
4. a(x+y)
  1. =ax+ay
5. https://www.mathsisfun.com/algebra/expanding.html
6. 3p(x+y)
  1. =3px+3py
7. 2(4x+y)+8(3x+2y)
  1. =8x+2y+24x-16y
    1. =32x-18y
8. Each term inside the brackets is multiplied by the term outside.
9. You can always check expanding by factorising
Patterns
Co-ordinates
1. We use coordinates to describe the position of points
2. The axes are at right angles to each other
3. Both scales are like number lines, evenly spaced
4. The horizontal axes is called the x axis
  1. The vertical axis is called the y axis
5. The y axis is always listed first
  1. The person goes down the corridor and up the stairs
6. Rise over run
  1. y=2x
    1. 2/1
      1. 2 up, 1 across
Factorising
1. Factorising is the reverse process of expanding.
  1. Instead of taking it out of brackets it is putting them back in them
2. Look for the Highest common factor in all terms
3. http://www.myimaths.com/tasks/library/loadLesson.asp?title=factorising/factoriseExpressions&taskID=1155
4. 2x+2y=2(x+y)
5. 3x+12=3(x+4)
6. 6x-15=3(2x-5)
7. cd-ce=c(d-e)
8. x^2-xy=x(x-y)
9. You can always check factorising by expanding
Solving Equations
1. Equations give information about the values of unknown numbers
2. We use x to represent the unknown number
3. Use the opposite operation to solve an equation
  1. ➕ to ➖ and ➖ to ➕
  2. ➗ to ✖ and ✖ to ➗
4. 4x=20
  1. x=20/4
    1. x=5
5. x+3=10
  1. x=10-3
    1. x=7
6. x/3=2
  1. x=3x2
    1. x=6
7. x-8=3
  1. x=3+8
    1. x=11
8. Combined Equations
  1. Collect all x terms on the left hand side.
    1. Collect all numbers on the right side.
  2. 6x-5=13
    1. 6x=13+5
      1. 6x=18
        x=18/6
        x=3
  3. 8x+12=20
    1. 8x=20-12
      1. 8x=8
        x=8/8
        x=1
Simplifying

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