question_answer 10)

Subtract: (i) \[-5{{y}^{2}}\] from \[{{y}^{2}}\]                                                         (ii) \[6xy\] from \[-12xy\] (iii) \[(a-b)\] from \[(a+b)\]                                                        (iv) \[a(b-5)\] from \[b(5-a)\] (v) \[-{{m}^{2}}+5mn\] from  \[4{{m}^{2}}-3mn+8\]                        (vi) \[-{{x}^{2}}+10x-5\] from \[5x-10\] (vii) \[5{{a}^{2}}-7ab+5{{b}^{2}}\] from  \[3ab-2{{a}^{2}}-2{{b}^{2}}\]      (viii) \[4pq-5{{q}^{2}}-3{{p}^{2}}\] from \[5{{p}^{2}}+3{{q}^{2}}-pq\]

Answer:

                (i) \[\mathbf{-5}{{\mathbf{y}}^{\mathbf{2}}}\] from \[{{\mathbf{y}}^{\mathbf{2}}}\]                 \[{{y}^{2}}-(-5{{y}^{2}})={{y}^{2}}+5{{y}^{2}}=6{{y}^{2}}\].                 (ii) \[\mathbf{6xy}\] from \[\mathbf{-12xy}\]                 \[-12xy-6xy=-18xy\]                 (iii) \[\mathbf{(a-b)}\] from \[\mathbf{(a+b)}\]                 \[(a+b)-(a-b)=a+b-a+b\]                 \[=a-a+b+b\]                                                                     \[\left| \text{rearranging terms} \right.\]                 \[=2b\]                      (iv) \[\mathbf{a(b-5)}\] from \[\mathbf{b(5-a)}\] \[b(5-a)-a(b-5)=5b-ab-ab+5a\] \[=5a+5b-ab-ab\]                                                            \[\left| \text{rearranging terms} \right.\] \[=5a+5b-2ab\]                 (v) \[\mathbf{-}{{\mathbf{m}}^{\mathbf{2}}}\mathbf{+5mn}\]from\[\mathbf{4}{{\mathbf{m}}^{\mathbf{2}}}\mathbf{-3mn+8}\]                 \[4{{m}^{2}}-3mn+8-(-{{m}^{2}}+5mn)\]                 \[=4{{m}^{2}}-3mn+8+{{m}^{2}}-5mn\]                 \[=4{{m}^{2}}+{{m}^{2}}-3mn-5mn+8\]                                 \[\left| \text{rearranging terms} \right.\] \[=5{{m}^{2}}-8mn+8\]                 (vi) \[\mathbf{-}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+10x-5}\] from \[\mathbf{5x-10}\]                 \[5x-10-(-{{x}^{2}}+10x-5)\] \[=5x-10+{{x}^{2}}-10x+5\] \[={{x}^{2}}+5x-10x-10+5\]                                                         \[\left| \text{rearranging terms} \right.\]             \[={{x}^{2}}-5x-5\]                 (vii) \[\mathbf{5}{{\mathbf{a}}^{\mathbf{2}}}\mathbf{-7ab+5}{{\mathbf{b}}^{\mathbf{2}}}\]  from \[\mathbf{3ab-2}{{\mathbf{a}}^{\mathbf{2}}}\mathbf{-2}{{\mathbf{b}}^{\mathbf{2}}}\]                 \[3ab-2{{a}^{2}}-2{{b}^{2}}-(5{{a}^{2}}-7ab+5{{b}^{2}})\]                 \[=3ab-2{{a}^{2}}-2{{b}^{2}}-5{{a}^{2}}+7ab-5{{b}^{2}}\]                 \[=-2{{a}^{2}}-5{{a}^{2}}-2{{b}^{2}}-5{{b}^{2}}+3ab+7ab\]                            \[\left| \text{rearranging terms} \right.\] \[=-7{{a}^{2}}-7{{b}^{2}}+10ab.\] (viii) \[\mathbf{4pq-5}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{-3}{{\mathbf{p}}^{\mathbf{2}}}\] from \[\mathbf{5}{{\mathbf{p}}^{\mathbf{2}}}\mathbf{+3}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{-pq}\] \[5{{p}^{2}}+3{{q}^{2}}-pq-(4pq-5{{q}^{2}}-3{{p}^{2}})\] \[=5{{p}^{2}}+3{{q}^{2}}-pq-4pq+5{{q}^{2}}+3{{p}^{2}}\] \[=5{{p}^{2}}+3{{p}^{2}}+3{{q}^{2}}+5{{q}^{2}}-pq-4pq\]                              \[\left| \text{rearranging terms} \right.\] \[=8{{p}^{2}}+8{{q}^{2}}-5pq.\]