FACTORISATION

Factorisation

a) By taking out common factors
b) By grouping
c) Of a different of two squares
d) By inspection or trial and error (quadratic) 

Example: Factorise the following expressions 
(i) by taking out common factors

(a) 2a + 4

Anwser =  2 (a + 2)

(b) 3x² y – xy²

Anwser = xy (3x – y)

(ii) by grouping

(a) ac + ad + 3c + 3d 

Anwser = a (c + d) + 3 (c + d)

(b) 3hk + ky – 3hy – kx 

Anwser = k (3h + y) – (3hy – kx)

(c) 3v – 6w + xv – 2xw

[3 x 2 = (6)]

Anwser = 3 (v – 2w) + x (v – 2w)

  

(iii) a difference of two factors 

(a) a² - 16

(16 = 4 x 4)

= a² – 4²

Final Anwser = (a + 4) (a - 4)

(b) 5k² – 125y²

^{(125 = 25 x 25)}

= 5 (x² – 25y²)

(25 = 5 x 5)

= 5 (x² – 5² y²)

Final Anwser = 5 (x + 5y) (x – 5y)

Questions that you can try: 

1. 2y + 6

2. a ² - b ² - c ² + d ² - 2(ad - bc) 

3. 4x ² + 20 x +25

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