Algebra Revision Cards

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Expanding Brackets

You must multiply the expression outside the bracket by everything inside the bracket.

4(2y+y) = 8+4y

I got this by doing: 4 x 2 = 8

                            4 x y = 4y

3x(2x+5y) = 6x² + 15xy

I got this by doing: 3x x 2x = 6x² 

                            3x x 5 = 15xy

2x (x² + 2x + 1) = 2x³ + 4x²  + 2x

I got this by doing: 2x x x² = 2x³

                            2x x 2x = 4x²

                            2x x 1 = 2x

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Factorising

Factorising is the opposite of expanding brackets. 

4 x - 12 

= 4 (x - 3)

18 x + 3

= 3 (6x + 1)

a² + 3a

= a (a + 3) 


    x² + 6x + 8           You must think about what goes into the last number (e.g. 8)

=  (x + 2) (x + 4)                              In this instance, it would be 1 x 8 or 2 x 4  (You decide                                                                                                   this depending on which two                                                                                                                                           numbers add together to make the middle                                                                                                                       number)

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Factorising (Continued)

You need to write the expression with TWO brackets.

Factorising x² + bx + c

5 + 2 = 7                                  you need to find two numbers which add up to 7 AND multiply to make 10

5 x 2 = 10

x²  + 7x + 10

= (x + 5) (x + 2) 

x²  + 7x - 8 

- 1 x + 8 or  1 x - 8 

 - 4 x +2  or  4 x - 2

- 1 x + 8 because it comes to 7

= (x + 1) (x + 8)


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Difference of two squares

Example:

x²  - 16

= (x - 4) (x + 4)

- 4 and + 4 = 0 and so it cancels out the middle number that would usually be there

x²  - 64                                  x²  - 49                                  x²  - 81      

= (x + 8) (x - 8)                      = (x + 7) (x - 7)                       = (x + 9) (x - 9)

 

a² - b²

= (a + b) (a - b)

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Linear Equations

To solve a linear equation you need to get the letter on it's own.

(- 3)    5x + 3 = 18                          

(÷ 5)         5x = 15

                  x = 3

Letter on both sides?                                   Equations with brackets 

(+ 2x)     2 - 2x = 26 + 4x                               Always start by multiplying out the brackets

(- 26)             2 = 26 + 6x                                19 = 8 - 2 (5 - 3y)     

(÷ 6)          - 24 = 6x                                       18 = 8 - 10 + 6y (+ because two minus')  

                   - 4 = x                                         19 = - 2 + 6y      (+ 2)      

                                                                                         19 = 6y              (÷ 6)

                                                                                          21/6  = y  meaning  y = 3.5

                                                                                          

 

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