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) \[\text{Sum}={{x}^{2}}-{{y}^{2}}-1+{{y}^{2}}-1-{{x}^{2}}+1-{{x}^{2}}-{{y}^{2}}\] \[={{x}^{2}}-{{x}^{2}}-{{x}^{2}}+{{y}^{2}}-{{y}^{2}}-{{y}^{2}}+1-1-1\] \[\left| \text{rearranging terms} \right.\] \[={{x}^{2}}+{{y}^{2}}+1\].
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