Special cases of factorising
Answers are for parents and teachers.
1
Factorise x² − 12x + 36.
(x − 6)².
2
Find k so that 4x² + kx + 49 is a perfect square (two answers).
The roots are 2x and 7, so the middle term is ±2 × 2x × 7 = ±28x and k = ±28.
3
Factorise 25x² − 36y² and 5x² − 20.
(5x − 6y)(5x + 6y) and 5(x − 2)(x + 2).
4
Find 63 × 57 using 60² − 3².
3600 − 9 = 3591.
5
Factorise 27x³ + 8.
(3x + 2)(9x² − 6x + 4).