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Question 5:
(a) Add: p (p − q), q (q − r) and r (r − p)
(b) Add: 2x (z − x − y) and 2y (z − y − x)
(c) Subtract: 3l (l − 4m + 5n) from 4l (10n − 3m + 2l)
(d) Subtract: 3a (a + b + c) − 2b (a − b + c) from 4c (− a + b + c)
Second expression = q (q − r) = q2 − qr
Third expression = r (r − p) = r2 − pr
Adding the three expressions, we obtain
Therefore, the sum of the given expressions is p2 + q2 + r2 − pq − qr − rp.
(b) First expression = 2x (z − x − y) = 2xz − 2x2 − 2xy
Second expression = 2y (z − y − x) = 2yz − 2y2 − 2yx
Adding the two expressions, we obtain
Therefore, the sum of the given expressions is − 2x2 − 2y2 − 4xy + 2yz + 2zx.
(c) 3l (l − 4m + 5n) = 3l2 − 12lm + 15ln
4l (10n − 3m + 2l) = 40ln − 12lm + 8l2
Subtracting these expressions, we obtain
Therefore, the result is 5l2 + 25ln.
(d) 3a (a + b + c) − 2b (a − b + c) = 3a2 +3ab + 3ac − 2ba + 2b2 − 2bc
= 3a2 + 2b2 + ab + 3ac − 2bc
4c (− a + b + c) = − 4ac + 4bc + 4c2
Subtracting these expressions, we obtain
Therefore, the result is −3a2 −2b2 + 4c2 − ab + 6bc − 7ac.
