Factorise the following expressions. (i) 7x - 42

(i) 7x – 42 

(ii) 6p-12q

(iii) 7a2 + 14a

(iv) -16z + 20z3

(v) 20l2m + 30alm

(vi) 5x2y – 15xy2

(vii) 10a2 – 15b2 + 20c2

(viii) -4a2 + 4ab – 4 ac

(ix) x2yz + xy2z+ xyz2

(x) ax2y + bxy2 + cxyz

Solution:

(i) 7x – 42 

Take 7 as common

= 7(x – 6)

(ii) 6p-12q = 6(p-2q)

(iii) 7a2 + 14a = 7a(a + 2)

(iv) -16z + 20z3 = 4z(-4 + 5z2)

(v) 20l2m + 30alm = 10lm(2l + 3a)

(vi) 5x2y – 15xy2 = 5xy(x – 3y)

(vii) 10a2 – 15b2 + 20c2 = 5(2a2 – 3b2 + 4c2)

(viii) -4a2 + 4ab – 4 ac = 4a(-a + b – c)

(ix) x2yz + xy2z+ xyz2 = xyz(x + y + z)

(x) ax2y + bxy2 + cxyz = xy(ax + by + cz)

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