question_answer 1)

                Obtain the product of                 (i) \[xy,\,yz,\,zx\]                 (ii) \[a,\,-{{a}^{2}},\,{{a}^{3}}\]                 (iii) \[2,\,4y,\,8{{y}^{2}},\,16{{y}^{3}}\]                 (iv) \[a,\,2b,\,3c,\,6abc\]                 (v) \[m,\,-mn,\,mnp\].

Answer:

                (i) \[xy,\,yz,\,zx\] Required product \[=(xy)\times (yz)\times (zx)\] \[=(x\times x)\times (y\times y)\times (z\times z)\] \[={{x}^{2}}\times {{y}^{2}}\times {{z}^{2}}\] \[={{x}^{2}}{{y}^{2}}{{z}^{2}}\]                 (ii) \[a,\,-{{a}^{2}},\,{{a}^{3}}\] Required product \[=(a)\times \,(-{{a}^{2}})\,\times ({{a}^{3}})\] \[=-(a\times {{a}^{2}}\times {{a}^{3}})\] \[=-{{a}^{6}}\]                 (iii) \[2,\,4y,\,8{{y}^{2}},\,16{{y}^{3}}\] Required product \[=(2)\times (4y)\times (8{{y}^{2}})\times (16{{y}^{3}})\] \[=(2\times 4\times 8\times 16)\times (y\times {{y}^{2}}\times {{y}^{3}})\] \[=1024{{y}^{6}}\] (iv) \[a,\,2b,\,3c,\,6abc\] Required product \[=(a)\times (2b)\times (3c)\times (6abc)\] \[=(2\times 3\times 6)\times (a\times a)\times (b\times b)\]\[\times (c\times c)\] \[=36{{a}^{2}}{{b}^{2}}{{c}^{2}}\] (v) \[m,\,-mn,\,mnp\] Required product \[=(m)\times (-mn)\times (mnp)\] \[=(-1)\times (m\times m\times m)\]\[\times (n\times n)\times p\] \[=-{{m}^{3}}{{n}^{2}}p\].