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# 2. Factorise the following expressions. (i) $$7x – 42$$ (ii) $$6p – 12q$$ (iii) $$7a^2 + 14a$$ (iv) $$-16z + 20z^3$$ (v) $$20l^2m + 30alm$$ (vi) $$5x^2y – 15xy^2$$ (vii) $$10a^2 – 15b^2 + 20c^2$$ (viii) $$-4a^2 + 4ab – 4ca$$ (ix) $$x^2yz + xy^2z + xyz^2$$ (x) $$ax^2y + bxy^2 + cxyz$$

(i)We have: $$7x – 42 = 7(x – 6)$$

(ii)We have: $$6p – 12q = 6(p – 2q)$$

(iii) We have: $$7a^2 + 14a = 7a(a + 2)$$

(iv)We have: $$-16z + 20z^3 = 4z(-4 + 5z^2)$$

(v) We have: $$20l^2m + 30alm = 10lm(2l + 3a)$$

(vi) We have: $$5x^2y – 15xy^2 = 5xy(x – 3y)$$

(vii) We have: $$10a^2 – 15b^2 + 20c^2 = 5(2a^2 – 3b^2 + 4c^2)$$

(viii)We have: $$-4a^2 + 4ab – 4ca = 4a(-a + b – c)$$

(ix)We have: $$x^2yz + xy^2z + xyz^2 = xyz(x + y + z)$$

(x) We have: $$ax^2y + bxy^2 + cxyz = xy(ax + by + cz)$$