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8th Class Mathematics Sample Paper Mathematics Sample Paper - 8

  • question_answer
    Show that: \[{{(4pq+3q)}^{2}}-{{(4pq-3q)}^{2}}=48p{{q}^{2}}\]

    Answer:

    L.H.S =\[{{(4pq+3q)}^{2}}-{{(4pq-3q)}^{2}}\]
    \[={{(4pq)}^{2}}+2(4pq)(3q)+{{(3q)}^{2}}-[{{(4pq)}^{2}}-2(4pq)(3q)+{{(3q)}^{2}}]\]                                                                    
    \[=16{{p}^{2}}{{q}^{2}}+24p{{q}^{2}}+9{{q}^{2}}-[16{{p}^{2}}{{q}^{2}}-24p{{q}^{2}}+9{{q}^{2}}]\]
    \[=16{{p}^{2}}{{q}^{2}}+24p{{q}^{2}}+9{{q}^{2}}-16{{p}^{2}}{{q}^{2}}+24p{{q}^{2}}-9{{q}^{2}}\]                                                                              
    \[=48p{{q}^{2}}=R.H.S\]


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