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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) \(ax^2y + bxy^2 + cxyz\)


Answer :

(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: \(ax^2y + bxy^2 + cxyz = xy(ax + by + cz)\)