多項式 數學題(20點)

1) 化簡m(m^2)^3(m^4)5=m*ｍ6*m^20=m^27
2) 化簡(p^3)^6/p^5=p^18/p^5=p^13
3)化簡(AB^2)^3˙a^2/b=a^3 b^6*a^2/b=a^5/b^7
4)化簡(r/s^3)^2 s/r5=(r^2/s^60*(s/r^5)=1/(r^3 s^5)
5)化簡8^2x˙16^y=2^6x*2^4y=2^(6x+4y)
6)化簡27^m/9^2n=27^m*9^-2n=3^3m*3^-4n=3^(3m-4n)
7)化簡(x^2+2x)+(3x^2-6x)=4x^2-4x
8)化簡(x^3+4x^2-8x)-(2x^3+x^2-6x)=-x^3+3x^2-2x
9)化簡(8x+3)+(3x-4)-(7-2x)=13x-8
10)化簡(-5a+6b)-(4b-2c)+(5c-7a)=-12a+2b+7c
11)展開2x(5x-6)=10x^2-12x
12)展開(x+5)(2x-1)2x^2+9x-5
13)展開(2x+3y)(x-4y)=2x^2-5xy-12y^2
14)展開(x^2+4x-2)(3x-4)=3x^3+8x^2-22x+8
15)展開(x-6)^2=x^2-12x-36
16)展開(x+7)(x-7)=x^2-49

1) 化簡m(m^2)^3(m^4)5

m(m^2)^3(m^4)5
=m*m^6*m^20
=m^(1＋6＋20)
=m^27

2) 化簡(p^3)^6/p^5,並以正指數表示答案

(p^3)^6/p^5
=p^18/p^5
=p^(18－5)
=p^13

3)化簡(AB^2)^3˙a^2/b

(AB^2)^3˙a^2/b
=(A^2B^6)*(a^2/b)

4)化簡(r/s^3)^2 s/r5

(r/s^3)^2* (s/r^5)
=(r^2/s^6)*(s/r^5)
=r^(2－5)*s^(1－6)
=r^－3*s^－5
=1/r^3s^5

5)化簡8^2x˙16^y

8^2x*16^y
=(2^3)^2x*(2^4)^y
=2^6x*2^4y
=2^(6x＋4y)

6)化簡27^m/9^2n

27^m/9^2n
=(3^3)^m/(3^2)^n
=3^3m/3^2n
=3^(3m－2n)

7)化簡(x^2+2x)+(3x^2-6x)

(x^2＋2x)＋(3x^2－6x)
=x^2＋3x^2＋2x－6x
=4x^2－4x
=4x(x－1)

8)化簡(x^3+4x^2-8x)-(2x^3+x^2-6x)

(x^3＋4x^2－8x)－(2x^3＋x^2－6x)
=x^3－2x^3＋4x^2－x^2－8x＋6x
=－x^3＋3x^2－2x
=－x(x^2－3x＋2)
=－x(x－2)(x－1)

9)化簡(8x+3)+(3x-4)-(7-2x)

(8x＋3)＋(3x－4)－(7－2x)
=8x＋3x＋2x＋3－4－7
=13x－8

10)化簡(-5a+6b)-(4b-2c)+(5c-7a)

(－5a＋6b)－(4b－2c)＋(5c－7a)
=－5a－7a＋6b－4b＋2c＋5c
=－12a＋2b＋7c

11)展開2x(5x-6)

2x(5x－6)
=10x^2－12x

12)展開(x+5)(2x-1)

(x＋5)(2x－1)
=x(2x－1)＋5(2x－1)
=2x^2－x＋10x－5
=2x^2＋9x－5

13)展開(2x+3y)(x-4y)

(2x＋3y)(x－4y)
=2x(x－4y)＋3y(x－4y)
=2x^2－8xy＋3xy－12y^2
=2x^2－5xy－12y^2

14)展開(x^2+4x-2)(3x-4),並以降冪法排列

(x^2＋4x－2)(3x－4)
=3x(x^2＋4x－2)－4(x^2＋4x－2)
=3x^3＋12x^2－6x－4x^2－16x＋8
=3x^3＋8x^2－22x＋8

15)展開(x-6)^2

(x－6)^2
=(x－6)(x－6)
=x(x－6)－6(x－6)
=x^2－6x－6x＋36
=x^2－12x＋36

16)展開(x+7)(x-7)

(x＋7)(x－7)
=x(x－7)＋7(x－7)
=x^2－7x＋7x－49
=x^2－49

2008-09-14 00:17:09 補充：
題目看錯重新修正
6)化簡27^m/9^2n

27^m/9^2n
=(3^3)^m/(3^2)^2n
=3^3m/3^4n
=3^(3m－4n)

步驟？...

布罩是?

1) 化簡m(m^2)^3(m^4)5=5m(m^6)(m^4)=5m^(1+6+4)=5m^11
2) 化簡(p^3)^6/p^5,並以正指數表示答案=p^18/p^5=p^(18-5)=p^13
3)化簡(AB^2)^3˙a^2/b=a^3˙b^6˙a^2/b=a^(3+2)˙b^(6-1)
=a^5˙b^5=(ab)^5
4)化簡(r/s^3)^2 s/r5=5r^2/s^6˙s/r=5r^(2-1)/s^(6-1)=5r/s^5
5)化簡8^2x˙16^y=(2^3)^2x˙(2^4)^y=2^(3˙2x)˙2^(4˙y)
=2^6x˙2^4y=2^(6x+4y)
6)化簡27^m/9^2n=3^3m/3^4n=3^(3m-4n)
7)化簡(x^2+2x)+(3x^2-6x)=(1+3)x^2+(2-6)x=4x^2-4x
8)化簡(x^3+4x^2-8x)-(2x^3+x^2-6x)=(1-2)x^3+(4-1)x^2+(-8+6)x
=-x^3+3x^2-2x
9)化簡(8x+3)+(3x-4)-(7-2x)=(8+3+2)x+(3-4-7)=13x-8
10)化簡(-5a+6b)-(4b-2c)+(5c-7a)=(-5-7)a+(6-4)b+(2+5)c
=-12a+2b+7c
11)展開2x(5x-6)=10x^2-12x
12)展開(x+5)(2x-1)=2x^2-x+10x-5=2x^2+9x-5
13)展開(2x+3y)(x-4y)=2x^2-8xy+3xy-12y^2=2x^2-5xy-12y
14)展開(x^2+4x-2)(3x-4),並以降冪法排列
=3x^3-4x^2+12x^2-16x-6x+8=3x^3+8x^2-22x+8
15)展開(x-6)^2=x^2-2˙x˙6+6^2=x^2-12x+36
16)展開(x+7)(x-7)=x^2-7^2=x^2-49

2008-09-14 13:44:55 補充：
題目打錯了,重新修正
1)化簡m(m^2)^3(m^4)^5=m(m^6)(m^20)=m^(1+6+20)=m^27
4)化簡(r/s^3)^2 s/r^5=r^2/s^6s/r^5=1/(r^3*s^5)