question_answer 1)

Add: (i) \[3mn,-5mn,8mn,-4mn\] (ii) \[t-8tz,3tz-z,z-t\] (iii) \[-7mn+5,12mn+2,9mn-8,-2mn-3\] (iv) \[a+b-3,b-a+3,a-b+3\] (v) \[14x+10y-12xy-13,18-7x-10y\]\[+8xy,\]\[4xy\] (vi) \[5m-7n,3n-4m+2,2m-3mn-5\] (vii) \[4{{x}^{2}}y,-3x{{y}^{2}}-5x{{y}^{2}},5{{x}^{2}}y\] (viii) \[3{{p}^{2}}{{q}^{2}}-4pq+5,-10{{p}^{2}}{{q}^{2}},15+9pq\]\[+7{{p}^{2}}{{q}^{2}}\] (ix) \[ab-4a,4b-ab;4a-4b\] (x) \[{{x}^{2}}-{{y}^{2}}-1,{{y}^{2}}-1-{{x}^{2}},1-{{x}^{2}}-{{y}^{2}}\]

Answer:

                (i) \[\text{Sum = 3mn + (-5mn) + 8mn + (- 4mn)}\]                 \[=3mn-5mn+8mn-4mn\]                 \[=3mn+8mn-5mn-4mn\]                                                                            \[\left| \text{rearranging terms} \right.\]                \[=11mn-9mn=2mn\]                 (ii) \[\text{Sum}=t-8tz+3tz-z+z-t\]                 \[=t-t-8tz+3tz-z+z\]                                                                                        \[\left| \text{rearranging terms} \right.\]                 \[=0-5tz-0=-5tz.\]                 (iii) \[\text{Sum}=-7mn+5+12mn+2+9mn+(-8)\]\[+(-2mn-3)\] \[=-7mn+5+12mn+2+9mn-8-2mn-3\] \[=-7mn+12mn+9mn-2mn+5+2-8-3\]                                     \[\left| \text{rearranging terms} \right.\] \[=12mn+9mn-7mn-2mn+5+2-8-3\]                                        \[\left| \text{rearranging terms} \right.\] \[=21mn-9mn+7-11\] \[=12mn-4.\]                 (iv) \[\text{Sum}=a+b-3+b-a+3+a-b+3\]                 \[=a-a+a+b+b-b-3+3+3\]                                                                              \[\left| \text{rearranging terms} \right.\] \[=a+a-a+b+b-b+3+3-3\]                                                                              \[\left| \text{rearranging terms} \right.\] \[=a+b+3\].                 (v) \[\text{Sum}=14x+10y-12xy-13+18-7x-10y\]\[+8xy+4xy\] \[=8xy+4xy-12xy+14x-7x+10y-10y\]\[+18-13\]                   \[\left| \text{rearranging terms} \right.\] \[=7x+5\].                 (vi) \[\text{Sum}=5m-7n+3n-4m+2+2m\]\[-3mn-5\]                 \[=5m+2m-4m+3n-7n+2-5-3mn\]                                                             \[\left| \text{rearranging terms} \right.\] \[=3m-4n-3-3mn.\]                 (vii) \[\text{sum}=4{{x}^{2}}y+(-3x{{y}^{2}})+(-5x{{y}^{2}})+5{{x}^{2}}y\]                 \[=4{{x}^{2}}y-3x{{y}^{2}}-5x{{y}^{2}}+5{{x}^{2}}y\]                                                                        \[\left| \text{rearranging terms} \right.\] \[=4{{x}^{2}}y+5{{x}^{2}}y-3x{{y}^{2}}-5x{{y}^{2}}\]                                                                        \[\left| \text{rearranging terms} \right.\] \[=9{{x}^{2}}y-8x{{y}^{2}}\]                 (viii) \[\text{Sum}=3{{p}^{2}}{{q}^{2}}-4pq+5+(-10{{p}^{2}}{{q}^{2}})\]\[+(15+9pq+7{{p}^{2}}{{q}^{2}})\] \[=3{{p}^{2}}{{q}^{2}}-4pq+5-10{{p}^{2}}{{q}^{2}}+15+9pq+7{{p}^{2}}{{q}^{2}}\] \[=3{{p}^{2}}{{q}^{2}}+7{{p}^{2}}{{q}^{2}}-10{{p}^{2}}{{q}^{2}}+9pq-4pq+5+15\]                                              \[\left| \text{rearranging terms} \right.\] \[=5pq+20.\]                 (ix) \[\text{Sum}=ab-4a+4b-ab+4a-4b\] \[=ab-ab+4a-4a+4b-4b\]                                                                              \[\left| \text{rearranging terms} \right.\] \[=0\].                 (x) \[\text{Sum}={{x}^{2}}-{{y}^{2}}-1+{{y}^{2}}-1-{{x}^{2}}+1-{{x}^{2}}-{{y}^{2}}\]                 \[={{x}^{2}}-{{x}^{2}}-{{x}^{2}}+{{y}^{2}}-{{y}^{2}}-{{y}^{2}}+1-1-1\]                                                        \[\left| \text{rearranging terms} \right.\] \[={{x}^{2}}+{{y}^{2}}+1\].