EXPANSION OF BRACKETS - ANSWERS

1. (2 - x) (4 - x)

= 8 -2x -4x +x2
= x2 -6x + 8
2. (2x - 1) (3x + 2)
 = 6x2 +4x -3x -2
= 6x2 + x - 2
3. (3x - 4y)2

= (3x - 4y) (3x - 4y)
= 9x2 -12xy -12yx +16y2
= 9x2 -24xy + 16y2

(Note: -12xy is the same as -12yx)
4. (2 - 5x) (3 - x)

= 6 -2x -15x +5x2
= 5x2 -17x + 6

(Note: it's conventional to write the higher terms first - i.e. those with the largest indicies)
5. (2a - 4b) (a + 2b) = 2a2 +4ab -4ba -8b2
= 2a2 - 8b2
6. (x2 - 2x)2 = (x2 - 2x) (x2 - 2x)
= x4 -2x3 -2x3 +4x2
= x4 -4x3 +4x2
7. (4x2y3)2 = (4x2y3) (4x2y3)
= 16x4y6
8. (x + y)2 = (x + y) (x + y)
= x2 + xy +yx + y2
= x2 + 2xy + y2