CHAPTER 8 — EXERCISE 8.1
1. Add the following.
(i) Add: \(ab - bc,\; bc - ca,\; ca - ab\)
Step 1:
Write the sum and group like terms: \((ab - bc) + (bc - ca) + (ca - ab)\).
Final answer: \(0\)
(ii) Add: \(a - b + ab,\; b - c + bc,\; c - a + ac\)
Step 1:
Write sum, expand and cancel linear terms; collect product terms.
Final answer: \(ab + bc + ac\)
(iii) Add: \(2p^{2}q^{2} - 3pq + 4\) and \(5 + 7pq - 3p^{2}q^{2}\)
Step 1:
Write both expressions side by side and group like terms by powers of \(p\) and \(q\).
Final answer: \(-\,p^{2}q^{2} + 4pq + 9\)
(iv) Add: \(l^{2}+m^{2},\; m^{2}+n^{2},\; n^{2}+l^{2},\; 2lm+2mn+2nl\)
Step 1:
List squares and pair-products; combine like terms and factor common factor if any.
Final answer: \(2(l^{2}+m^{2}+n^{2}+lm+mn+nl)\)
2. Subtract the following.
(a) Subtract \(4a - 7ab + 3b + 12\) from \(12a - 9ab + 5b - 3\).
Step 1:
Set up the subtraction \( (12a - 9ab + 5b - 3) - (4a - 7ab + 3b + 12)\) and change signs for terms in the second group.
Final answer: \(8a - 2ab + 2b - 15\)
(b) Subtract \(3xy + 5yz - 7zx\) from \(5xy - 2yz - 2zx + 10xyz\).
Step 1:
Write both expressions, remove parentheses and then group like terms (xy, yz, zx, xyz).
Final answer: \(2xy - 7yz + 5zx + 10xyz\)
(c) Subtract \(4p^{2}q - 3pq + 5pq^{2} - 8p + 7q - 10\) from \(18 - 3p - 11q + 5pq - 2pq^{2} + 5p^{2}q\).
Step 1:
Arrange terms, change signs for the second bracket, and combine like terms carefully (watch signs).
Final answer: \(p^{2}q + 8pq - 7pq^{2} + 5p - 18q + 28\)
Created and Designed by Zahid Qayoom