question_answer 1)

                Add the following:                 (i) \[ab-bc,\,bc-ca,\,ca-ab\] (ii) \[a-b+ab,\,b-c+bc,\,c-a+ac\] (iii) \[2{{p}^{2}}{{q}^{2}}-3pq+4,\,5+7pq-3{{p}^{2}}{{q}^{2}}\] (iv) \[{{l}^{2}}+{{m}^{2}},\,{{m}^{2}}+{{n}^{2}},\,{{n}^{2}}+{{l}^{2}},\,2lm\,+2mn+2nl\].

Answer:

                (i) \[ab-bc,\,bc-ca,\,ca-ab\]

	\[ab-bc\]
+		\[+bc-ca\]
+	\[-ab\]		\[ca\]
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(ii) \[a-b+ab,\,b-c+bc,\,c-a+ac\]

	\[a-b+ab\]
+	\[+b\]	\[-c+bc\]
+	\[-a\]	\[+c\]	\[+ac\]
\[ab+bc\]\[+ac\]

(iii) \[2{{p}^{2}}{{q}^{2}}-3pq+4,\,5+7pq-3{{p}^{2}}{{q}^{2}}\]

	\[2{{p}^{2}}{{q}^{2}}-3pq+4\]
+	\[-3{{p}^{2}}{{q}^{2}}+7pq+5\]
\[-{{p}^{2}}{{q}^{2}}+4pq+9\]

(iv) \[{{l}^{2}}+{{m}^{2}},\,{{m}^{2}}+{{n}^{2}},\,{{n}^{2}}+{{l}^{2}},\,2lm\,+2mn+2nl\].

	\[{{l}^{2}}+{{m}^{2}}\]
+		\[+{{m}^{2}}+{{n}^{2}}\]
+	\[{{l}^{2}}\]	\[+{{n}^{2}}\]
+			\[+2lm+2mn+2nl\]
\[2{{l}^{2}}+2{{m}^{2}}+2{{n}^{2}}+2lm\,+2mn\,+2nl\] \[=2({{l}^{2}}+{{m}^{2}}+{{n}^{2}}+lm\,+mn\,+nl)\]