question_answer 12)

(a) From the sum of \[3x-y+11\] and \[-y-11,\] subtract \[3x-y-11\]. (b) From the sum of \[4+3x\] and \[5-4x+2{{x}^{2}},\] subtract the sum of \[3{{x}^{2}}-5x\] and \[-{{x}^{2}}+2x+5\].

Answer:

                (a) Resulting expression                 \[=\{(3x-y+11)+(-y-11)\}-(3x-y-11)\]                 \[=3x-y+11-y-11-3x+y+11\]                 \[=3x-3x+y-y-y+11+11-11\]                         \[\left| \text{rearranging terms} \right.\] \[=-y+11.\]                 (b) Resulting expression                 \[=\{(4+3x)+{{(5-4x+2x)}^{2}}\}\]\[-\{(3{{x}^{2}}-5x)+(-{{x}^{2}}+2x+5)\}\] \[=4+3x+5-4x+2{{x}^{2}}-3{{x}^{2}}+5x\]\[+{{x}^{2}}-2x-5\] \[=2{{x}^{2}}+{{x}^{2}}-3{{x}^{2}}+3x+5x-2x-4x\]\[+4+5-5\] \[=2x+4\].