Exercise 8.1
1. Add the following:
(i) ab – bc, bc – ca, ca – ab
(ab – bc) + (bc – ca) + (ca - ab) = ab – bc + bc – ca + ca – ab
= ab – ab – bc + bc – ca + ca (Rearranging) =
(ii) a – b + ab, b – c + bc, c – a + ac
a – b + ab + b – c + bc + c – a + ac = a – a +b – b +c – c + ab + bc + ca (rearranging)
=
(iii) 2 p 2 q 2 − 3 pq + 4 , 5 + 7 pq − 3 p 2 q 2
=
(iv) l 2 + m 2 m 2 + n 2 n 2 + l 2 2 lm + 2 mn + 2 nl
=
2. (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
(12a – 9ab + 5b – 3) – (4a – 7ab + 3b + 12) = 12a – 9ab + 5b – 3 +
= 12a – 4a - 9ab + 7ab + 5b – 3b -3 -12 (rearranging)
=
(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
(5xy – 2yz – 2zx + 10xyz) – (3xy + 5yz – 7zx) = 5xy – 2yz – 2zx + 10xyz +
= 5xy – 3xy – 2yz – 5yz – 2zx + 7zx + 10xyz (rearranging)
=
(c) Subtract
= 18 – 3p – 11q + 5pq – 2 pq 2 5 p 2 q + p 2 q + pq 2
= 18 + 10 − 3 p + 8 p − 11 q − 7 q + 5 pq + 3 pq − 2 pq 2 − 5 pq 2 + 5 p 2 q − 4 p 2 q = pq 2 p 2 q