幼稚園都懂的數學乙題

16 (5x + 2y)^4 - 72 (5x + 2y)^2 (2x + y)(2x - y) + 81(2x + y)^2 (2x - y)^2
={4[(5x+2y)^2]-[9(2x+y)(2x-y)]}^2
={4(25x^2+20xy+4y^2)-9(4x^2-y^2)}^2
=[100x^2+80xy+16y^2-36x^2+9y^2]^2
=[64x^2+25y^2+80xy]^2
=[(8x+5y)^2]^2
=(8x+5y)^4

步驟好長,可能做錯嫁,最好自已對一對
ps這一題我自出娘胎就識(不是幼稚園都懂)........講笑姐

2007-12-25 22:26:27 補充：
你係咪講緊我係no.7呀如果係 = = 我又去計多一次我既答案都係(8x+5y)^4重新計一次既步驟16 (5x + 2y)^4 - 72 (5x + 2y)^2 (2x + y)(2x - y) + 81(2x + y)^2 (2x - y)^2=[4(25x^2+20xy+4y^2)-36x^2+9y^2]^2=(100x^2+80xy+16y^2-36x^2+9y^2]^2=(64x^2+80xy+25y^2)^2=[(8x+5y)^2]^2=(8x+5y)^4如果你計既答案同我唔同,不妨講出黎,大家討論下

2007-12-25 23:23:40 補充：
算啦,好慘慘慘慘慘慘慘慘呀唉,我以為你講我呀我頭先展開曬D式,你睇下啦16(5x 2y)^4=10000x^4 16000x^3y 9600x^2y^2 2560xy^3 256y^4-72(5x 2y)^2 (2x y)(2x - y) =-7200x^4-5760x^3y 648x^2y^2 1440xy^3 288y^481(2x y)^2 (2x - y)^2=1296x^4-648x^2y^2 81y^4重有

2007-12-25 23:25:36 補充：
16 (5x + 2y)^4 - 72 (5x + 2y)^2 (2x + y)(2x - y) + 81(2x + y)^2 (2x - y)^2=4096x^4+10240x^3y+1600x^2y^2+4000xy^3+652y^4(8x+5y)^4=4096x^4+10240x^3y+1600x^2y^2+4000xy^3+625y^4展開到我吐電 = =雖然用規律就好快計完(斷氣中..........)又多一個爛gag = ="

為方便計算，先設a=(5x + 2y)；b=(2x + y)(2x - y)。
16 (5x + 2y)^4 - 72 (5x + 2y)^2 (2x + y)(2x - y) + 81(2x + y)^2 (2x - y)^2
=16(a^4)-72(a^2)(b)+81b^2
=(4a^2)^2-2(4a^2)(9b)+(9b)^2
=(4a^2+9b)^2
代入a和b。
16 (5x + 2y)^4 - 72 (5x + 2y)^2 (2x + y)(2x - y) + 81(2x + y)^2 (2x - y)^2
=(4a^2+9b)^2
=[4(5x + 2y)^2+9(2x + y)(2x - y)]^2
=[4(5x + 2y)^2+9(4x^2-y^2)]^2
=[4(25x^2+20xy+4y^2)+9(4x^2-y^2)]^2
=(100x^2+80xy+16y^2+36x^2-9y^2)^2
=(136x^2+80xy+7y)^2