question_answer 10)

                Carry out the multiplication of the expressions in each of the following pairs:                 (i) \[4p+q+r\]                     (ii) \[ab,\,a-b\]                  (iii) \[a+b,\,7{{a}^{2}}{{b}^{2}}\]                                (iv) \[{{a}^{2}}-9,\,4a\]                 (v) \[pq+qr+2p,\,0\]

Answer:

                (i) \[4p+q+r\]                     \[(4p)\times (q+r)=(4p)\times (q)+(4p)\times (r)\] \[=4pq+4pr\]     8959781310 (ii) \[ab,\,a-b\] \[(ab)\times (a-b)=(ab)\times (a)-(ab)\times (b)\] \[={{a}^{2}}b-a{{b}^{2}}\]                 (iii) \[a+b,\,7{{a}^{2}}{{b}^{2}}\]                                \[(a+b)\times (7{{a}^{2}}{{b}^{2}})=(7{{a}^{2}}{{b}^{2}})\times (a+b)\]  |by commutative law \[(7{{a}^{2}}{{b}^{2}})\times (a)+(7{{a}^{2}}{{b}^{2}})\times (b)\] \[=7{{a}^{3}}{{b}^{2}}+7{{a}^{2}}{{b}^{3}}\] (iv) \[{{a}^{2}}-9,\,4a\] \[({{a}^{2}}-9)\,\times (4a)=(4a)\times ({{a}^{2}}-9)\]                     | by commutative law \[=(4a)\times ({{a}^{2}})-(4a)\times (9)\] \[=4{{a}^{3}}-36a\]                 (v) \[pq+qr+2p,\,0\] \[(pq+qr+2p)\times (0)\] \[=(0)\times (pq+qr+2p)\]                           |by commutative law \[=(0)\times (pq)+(0)\times (qr)+(0)\]\[\times (2p)\] \[=0+0+0\]                 = 0.