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 7a^{2} = 7 × a × a

Factor of -12q = 2 × 7× a

Common factors is 7, a = 7 × a = 7a

7a^{2}+14a = (7 × a × a)-( 2× 7 × a) = 7a(a-2)

(iv) Factor of -16z = - 2 × 2 × 2 × 2 × z

Factor of 20z^{3} = 2 × 2× 5 × z × z × z

Common factors is 2, 2, z = 2 × 2 × z = 4z

-16z+20z^{3} = -4z(z-5z^{2})

(v) Factor of 20l^{3}m = 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

20l^{3}m+30alm = 10lm(2l^{2}-3a)

(vi) Factor of 5x^{2}y = 5 × x × x × y

Factor of -15xy^{2} = -3 × 5 × x × y × y

Common factors is 5, x, y = 5 × x × y = 5xy

5x^{2}y-15xy^{2}= 5xy(x-3y)

(vii) Factor of 10a^{2} = 2 × 5 × a × a

Factor of -15b^{2} = -3 × 5 × b × b

Factor of 20c^{2} = 2 × 2 × 5 × c × c

Common factors is 5

10a^{2}-15b^{2}+20c^{2} = 5(2a^{2}-3b^{2}+c^{2})

(viii) Factor of -4a^{2} = -2 × 2 × a × a

Factor of 4ab = 2 × 2 × a × b

Factor of 4ca = 2 × 2 × c × a

Common factors is 2, 2, a

-4a^{2}+4ab-4ca = 4a(-a+b-c)

(ix) Factor of x^{2}yz = x × x × y × z

Factor of xy^{2}z = x × y × y × z

Factor of xyz^{2} = x × y × z × z

Common factors is x, y, z

X^{2}yz + xy^{2}z + xyz^{2} = xyz(z+y+z)

(x) Factor of ax^{2}y = a × x × x × y

Factor of bxy^{2} = b × x × y × y

Factor of cxyz = c × x × y × z

Common factors is x, y

a x^{2}y + bxy^{2} + cxyz = xy(ax+by+cz)

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