Factorise the following expressions.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii)
(viii)
(ix) 
(x) 
(i) Factor of 7x = 7 × x
Factor of 42 = 2× 3 × 7
Common factors is 7
7x-42 = (7× x)-( 2× 3 × 7) = 7(x-6)
(ii) Factor of 6p = 2 ×3 × p
Factor of -12q = -1× 2× 2 × 3 × q
Common factors is 2, 3 = 2× 3 = 6
6p-12q = (2 × 3 × p)-( 2× 2 × 3 × q) = 6(p-2q)
(iii) Factor of 7a2 = 7 × a × a
Factor of -12q = 2 × 7× a
Common factors is 7, a = 7 × a = 7a
7a2+14a = (7 × a × a)-( 2× 7 × a) = 7a(a-2)
(iv) Factor of -16z = - 2 × 2 × 2 × 2 × z
Factor of 20z3 = 2 × 2× 5 × z × z × z
Common factors is 2, 2, z = 2 × 2 × z = 4z
-16z+20z3 = -4z(z-5z2)
(v) Factor of 20l3m = 2 × 2 × 5 × l × l × l × m
Factor of 30alm = 2 × 3 × 5 × a × l × m
Common factors is 2, 5, l, m = 2 × 5 × l × m = 10lm
20l3m+30alm = 10lm(2l2-3a)
(vi) Factor of 5x2y = 5 × x × x × y
Factor of -15xy2 = -3 × 5 × x × y × y
Common factors is 5, x, y = 5 × x × y = 5xy
5x2y-15xy2= 5xy(x-3y)
(vii) Factor of 10a2 = 2 × 5 × a × a
Factor of -15b2 = -3 × 5 × b × b
Factor of 20c2 = 2 × 2 × 5 × c × c
Common factors is 5
10a2-15b2+20c2 = 5(2a2-3b2+c2)
(viii) Factor of -4a2 = -2 × 2 × a × a
Factor of 4ab = 2 × 2 × a × b
Factor of 4ca = 2 × 2 × c × a
Common factors is 2, 2, a
-4a2+4ab-4ca = 4a(-a+b-c)
(ix) Factor of x2yz = x × x × y × z
Factor of xy2z = x × y × y × z
Factor of xyz2 = x × y × z × z
Common factors is x, y, z
X2yz + xy2z + xyz2 = xyz(z+y+z)
(x) Factor of ax2y = a × x × x × y
Factor of bxy2 = b × x × y × y
Factor of cxyz = c × x × y × z
Common factors is x, y
a x2y + bxy2 + cxyz = xy(ax+by+cz)