- Factorise the following expressions
- 4x2 + 2y2 + x2y2 +8
- 25x2 + 4y2 + 20xy
1. 4x2 + 2y2 + x2y2 + 8 = 4x2 + 8 + 2y2 + x2y2
= 4 (x2 + 2) + y2 (2 + x2)
= (2 + x2) (4 + y2)
2. 25x2 + 4y2 + 20xy = 25x2 + 20xy + 4y2
= (5x)2 + 2(5x)(2y) + (2y)2
= (5x + 2y)2
= (5x + 2y) (5x + 2y)
= 4 (x2 + 2) + y2 (2 + x2)
= (2 + x2) (4 + y2)
2. 25x2 + 4y2 + 20xy = 25x2 + 20xy + 4y2
= (5x)2 + 2(5x)(2y) + (2y)2
= (5x + 2y)2
= (5x + 2y) (5x + 2y)