Notes for Factorisation

I. a^{2} + 2ab + b^{2} = (a + b)^{2}

II. a^{2} – 2ab + b^{2} = (a – b)^{2}

III. a^{2} – b^{2} = (a – b)(a + b)

IV. x^{2} + (a + b)x + ab = (x + a)(x + b)

(i) a^{2} + 2ab + b^{2} = (a + b)^{2}

(ii) a^{2} – 2ab + b^{2} = (a – b)^{2}

(iii) a^{2} – b^{2} = (a – b)(a + b)

(iv) 1 is a factor of every term of an algebraic expressionless it is specially required, we do not show I as a separate factor of any term.

(v) Factorisation means writing an expression as product Of factors.

For example, 6pq = 2 × 3 × pq is not the irreducible corm because pq can further be factorised as p × q, i.e. the irreducible fonn of 6pq = 2 × 3 × p × q.

xy = x × y

10xy = 2 × 5 × x × y