question_answer 8)

Simplify combining like terms: (i) \[21b-32+7b-20b\] (ii) \[-{{z}^{2}}+13{{z}^{2}}-5z+7{{z}^{3}}-15z\] (iii) \[p-(p-q)-q-(q-p)\] (iv) \[3a-2b-ab-(a-b+ab)+3ab+b-a\] (v) \[5{{x}^{2}}y-5{{x}^{2}}+3y{{x}^{2}}-3{{y}^{2}}+{{x}^{2}}-{{y}^{2}}\]\[+8x{{y}^{2}}-3{{y}^{2}}\] (vi) \[(3{{y}^{2}}+5y-4)-(8y-{{y}^{2}}-4)\]

Answer:

                (i) \[21b-32+7b-20b=21b+7b-20b-32\]                                                    \[\left| \text{rearranging terms} \right.\] \[=8b-32\] (ii) \[-{{z}^{2}}+13{{z}^{2}}-5z+7{{z}^{3}}-15z\]\[=13{{z}^{2}}-{{z}^{2}}\]\[-5z-15z+7{{z}^{3}}\].                    \[\left| \text{rearranging terms} \right.\] \[=12{{z}^{2}}-20z+7{{z}^{3}}\] (iii) \[p-(p-q)-q(q-p)=p-p+q-q-q\]\[+p\]\[=p+p-p+q-q-q\]    \[\left| \text{rearranging terms} \right.\] \[=p+q\].                 (iv) \[3a-2b-ab-(a-b+ab)+3ab+b-a\]                 \[=3a-2b-ab-a+b-ab+3ab+b-a\] \[=3a-a-a+b+b-2b+3ab-ab-ab\]                                                                 \[\left| \text{rearranging terms} \right.\] \[=a+ab\]                 (v) \[5{{x}^{2}}y-5{{x}^{2}}+3y{{x}^{2}}-3{{y}^{2}}+{{x}^{2}}-{{y}^{2}}\]\[+8x{{y}^{2}}\]\[-3{{y}^{2}}\] \[=5{{x}^{2}}y+3y{{x}^{2}}+{{x}^{2}}-5{{x}^{2}}-{{y}^{2}}-3{{y}^{2}}-3{{y}^{2}}+8x{{y}^{2}}\]                                                        \[\left| \text{rearranging terms} \right.\] \[=8{{x}^{2}}y-4{{x}^{2}}-7{{y}^{2}}+8x{{y}^{2}}\]                 (vi) \[3{{y}^{2}}+5y-4-(8y-{{y}^{2}}-4)\]                 \[=3{{y}^{2}}+5y-4-8y+{{y}^{2}}+4\]                 \[=3{{y}^{2}}+{{y}^{2}}+5y-8y-4+4\]                                                                                        \[\left| \text{rearranging terms} \right.\] \[=4{{y}^{2}}-3y\].