(a) Factorise the following expressions fully. (i) 10ab + 15b + 4a + 6 (ii) 6 x2
+ 9xy − 14x − 21y (iii) 5xy − 8x − 10y + 16 (b) Verify your factors for part (a)
8. Factorise the following expressions fully. (i) 12ab − 14a − 6b + 7 (ii) 6 x2
− 15x + 2xy − 5y (iii) 4a − 21 b2 + 6ab − 14b
9. Factorise the following expressions fully. (i) 8xy − 12y + 15 − 10x (ii) 7 + y − 3xy − 21x (iii) 32uv − 20u + 24v − 15
10. Find two expressions, one for the length and one for the width of a rectangle which has a total area represented by the following expression.
px + rs − pr − sx
11. Find two expressions, one for the length and one for the width of a rectangle which has a total area represented by the following expression.
12wx + 4wy + 6zx + 2zy
12. The area of a rectangular fi eld is given by the following expression:
10xy + 30 + 25x + 12y
Find an expression for the length and an expression for the width.
13. The number of chocolates Mary gives to Peter is described by one expression. The number of chocolates she gives to Judith is described by another expression. When Mary multiples the two expressions the result is: 56ab + 14 − 49a − 16b
Find an expression for the number of chocolates Mary gave to Peter and an expression for the number of chocolates she gave Judith.
14. When Dougal multiplies the expression that describes the amount of money that he gave Ted by the amount of money he gave Jack, the expression he gets is:
5mn + 2m − 25n − 10
Find an expression for the amount of money Dougal gave to Ted and an expression for the amount of money he gave Jack.
15. When the manager multiplies an expression that describes the number of rooms in her hotel by an expression that describes the
number of chairs in her hotel, she gets: 3mn − 8m + 15n − 40
Find an expression for the numbers of rooms and an expression for the number of chairs in the hotel.
Revision questions
20A Core skills 1. Write expressions for each of the following. (i) The sum of x and y (ii) Add a and 7 (iii) Twice b plus 10 (iv) The diff erence between m and n (v) The product of a and g
(vi) b cubed (vii) Triple x and add fi ve times the value of p (viii) Square x and subtract double x then add 7 (ix) The product of m and the square of c (x) 6 times m added to 2·5 times m
2. The express bus from Galway to Belfast takes x minutes. The standard bus takes 29 minutes longer. Write an expression for the time the standard bus takes.