Class VIII

Fully factorise after completing the square

Lesson

Worked examples

Question 1

Factorise the quadratic using the method of completing the square to get it into the form $y=\left(x+a\right)\left(x+b\right)$y=(x+a)(x+b).

$y=x^2+4x+3$y=x2+4x+3

Question 2

Factorise the quadratic using the method of completing the square to get it into the form $y=\left(x-a\right)\left(x-b\right)$y=(x−a)(x−b).

$y=x^2-11x+28$y=x2−11x+28

Question 3

Factorise the quadratic using the method of completing the square to get it into the form $y=\left(x+a+\sqrt{b}\right)\left(x+a-\sqrt{b}\right)$y=(x+a+√b)(x+a−√b).

$y=x^2+8x+14$y=x2+8x+14

Outcomes

8.A.AE.3

Identities (a ± b)^2 = a^2 ± 2ab + b^2, a^2 – b^2 = (a – b) (a + b) Factorisation (simple cases only) as examples the following types a(x + y), (x ± y)^2, a^2 – b^2, (x + a).(x + b)