8th Class Mathematics Algebraic Expressions - 854

  • question_answer 3)
                    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) \[ab-bc,\,bc-ca,\,ca-ab\]
    \[ab-bc\]
    + \[+bc-ca\]
    + \[-ab\] \[ca\]
    0
    (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) \[{{l}^{2}}+{{m}^{2}},\,{{m}^{2}}+{{n}^{2}},\,{{n}^{2}}+{{l}^{2}},\,2lm\,+2mn+2nl\].
    \[{{l}^{2}}+{{m}^{2}}\]
    + \[+{{m}^{2}}+{{n}^{2}}\]
    + \[{{l}^{2}}\] \[+{{n}^{2}}\]
    + \[+2lm+2mn+2nl\]
    \[2{{l}^{2}}+2{{m}^{2}}+2{{n}^{2}}+2lm\,+2mn\,+2nl\] \[=2({{l}^{2}}+{{m}^{2}}+{{n}^{2}}+lm\,+mn\,+nl)\]


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