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加法
(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). 4x2y, −3xy2, −5xy2, 5x2y
(viii). 3p2q2−4pq+5, −10p2q2, 15+9pq+7p2q2
(ix). ab−4a, 4b−ab, 4a−4b
(x). x2−y2−1, y2−1−x2, 1−x2−y2

需要完成的任务：求和

(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). 4x2y, −3xy2, −5xy2, 5x2y

(viii). 3p2q2−4pq+5, −10p2q2, 15+9pq+7p2q2

(ix). ab−4a, 4b−ab, 4a−4b

(x). x2−y2−1, y2−1−x2, 1−x2−y2


解答： 

i) 3mn, −5mn, 8mn, −4mn


=(3mn)+(−5mn)+(8mn)+(−4mn)


=(3−5+8−4)mn


=2mn


ii) t−8tz, 3tz−z, z−t


=(t−8tz)+(3tz−z)+(z−t)


=t−8tz+3tz−z+z−t


=t−t−8tz+3tz−z+z


=−5tz


iii) $– 7mn + 5 + 12mn + 2 + (9mn – 8) + (- 2mn – 3) = – 7mn + 5 + 12mn + 2 + 9mn – 8 – 2mn – 3$


=–7mn+12mn+9mn–2mn+5+2–8–3


=mn(−7+12+9–2)+(5+2–8–3)


=mn(−9+21)+(7–11)


=mn(12)–4


=12mn–4


iv) a+b−3, b−a+3, a−b+3


=(a+b−3)+(b−a+3)+(a−b+3)


=a−a+a+b+b−b−3+3+3


=a(1−1+1)+b (1+1−1)+3 (−1+1+1)


=a+b+3


v) 14x+10y−12xy−13, 18−7x−10y+8xy, 4xy


=(14x+10y−12xy−13)+(18−7x−10y+8yx)+4xy


=14x−7x+10y−10y−12xy+8yx+4xy−13+18


=x(14−7)+y(10−10)+xy (−12+8+4)−13+18


=7x+5


vi) 5m−7n, 3n−4m+2, 2m−3mn−5


=(5m−7n)+(3n−4m+2)+(2m−3mn−5)


=5m−4m+2m−7n+3n−3mn+2−5


=m(5−4+2)+n(−7+3)−3mn+2−5


=3m−4n−3mn−3


vii) 4x2y,−3xy2,−5xy2, 5x2y


=x2y (4+5)+xy2 (−3−5)


=9x2y−8xy2


viii) 3p2q2−4pq+5, −10p2q2, 15+9pq+7p2q2


=(3p2q2−4pq+5)+(−10p2q2)+(15+9pq+7p2q2)


=3p2q2−10p2q2+7p2q2−4pq+9pq+5+15


=p2q2(3−10+7)+pq(−4+9)+5+15


=5pq+20


ix) ab−4a, 4b−ab, 4a−4b


=(ab−4a)+(4b−ab)+(4a−4b)


=ab−ab−4a+4a+4b−4b


=ab(1−1)+a(−4+4)+b(4−4)


=0


x) x2−y2−1, y2−1−x2, 1−x2−y2


=(x2−y2−1)+(y2−1−x2)+(1−x2−y2)


=x2−x2−x2−y2+y2−y2−1−1+1


=x2 (1−1−1)+y2(−1+1−1)+(−1−1+1)


=−x2−y2−1

更新于： 2022年10月10日

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