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F.3 Factorization

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發問:

1. 49(a+b)^2-9(a-b)^2 2. -2(xz+yz-3z^2)+32(xz-2yz+z)^2 3. (y-2)^2-24(y-2)+144 4. 36(x-y)^2+12z(x-y)+z^2 5. 64x^2-8x-25y^2-5y 6. 80a^4-40a^2b^2+5b^4 7. x^2-2x+6xy-6y+9y^2 ***Factorize the above,thx ! (Reminder:they are not of the same type,some need to be factorized again,challenging!)

最佳解答:

1. 49(a+b)^2-9(a-b)^2 =49a^2+98ab+49b^2-9a^2+18ab-9b^2 =40a^2+116ab+40b^2 =4(10a^2+29ab+10b^2) =4(5a+2b)(2a+5b) e題拆開再砌返就搞掂 3. (y-2)^2-24(y-2)+144 Let x be y-2. x^2-24x+144 =(x-12)^2 =(y-2-12)^2 =(y-14)^2 e題let x會易計d 但計得多就唔駛再let 4. 36(x-y)^2+12z(x-y)+z^2 Let a be x-y. 36a^2+12za+z^2 =(6a)^2+2(6a)(z)+z^2 =(6a+z)^2 =(6(x-y)+z)^2 同上 5. 64x^2-8x-25y^2-5y =(8x)^2-8x-(5y)^2-5y =(8x+5y)(8x-5y)-(8x-5y) =(8x-5y)(8x-5y+1) e題砌砌下就做完 6. 80a^4-40a^2b^2+5b^4 =(√80a^2)^2-2(√80a^2)(√5b^2)+(√5b^2)^2 =(√80a^2-√5b^2)^2 夾硬砌 仲可以用a^2-b^2 繼續fact 但本人懶唔想打咁多字.. 7. x^2-2x+6xy-6y+9y^2 =x^2+2(x)(3y)+(3y)^2-2x-6y =(x+3y)^2-2(x+3y) =(x+3y)(x+3y-2) e題砌砌下就做完 第2題唔知係我廢得濟定係你抄錯題目.. 所以冇做 hope i can help u :) 2013-07-30 00:12:55 補充： 6. 80a^4-40a^2b^2+5b^4 =(√80a^2)^2-2(√80a^2)(√5b^2)+(√5b^2)^2 =(√80a^2-√5b^2)^2 =(4√5a^2)-√5b^2)^2 =5(4a^2-b^2)^2 =5((2a)^2-b^2)^2 =5(2a+b)^2(2a-b)^2 not the best way should take out 5 at the very beginning :(

其他解答:

Please read my answers as follows, hope that you can understand the tricks. 圖片參考：http://imgcld.yimg.com/8/n/HA00430218/o/20130729232230.jpg