中二數學,,,,急

1. (a+1)(a^2-a+1)
= a(a^2-a+1) + (a^2-a+1)
= (a^3-a^2+a) + (a^2-a+1)
= a^3 + 1

2. (x-y)(x^2+xy+y^2)
= x(x^2+xy+y^2) - y(x^2+xy+y^2)
= x^3+x^2 y+xy^2 - y(x^2+xy+y^2)
= x^3+x^2 y+xy^2 - x^2 y - xy^2 - y^3
= x^3 - y^3


3. (m+2)(m^2-2m+4)
= m(m^2-2m+4) + 2(m^2-2m+4)
= m^3-2m^2+4m + 2m^2-4m+8
= m^3 + 8

4. (a-2b)(a^2+2ab+4b^2)
= a(a^2+2ab+4b^2) -2b(a^2+2ab+4b^2)
= a^3+2a^2 b+4ab^2 -2b(a^2+2ab+4b^2)
= a^3+2a^2 b+4ab^2 -2a^2 b - 4ab^2 - 8b^3
= a^3 - 8b^3


5. (a^2+b)(a^4-a^2b+b^2)
= a^2(a^4-a^2b+b^2) + b(a^4-a^2b+b^2)
= a^6 - a^4 b + a^2 b^2 + a^4 b - a^2 b^2 + b^3
= a^6 + b^3

6. (a^2-b^2)(a^4+a^2b^2+b^4)
= (a^2)^3 - (b^2)^3
= a^6 - b^6

7. (x-1)^2(x^2+x+1)^2
= [(x-1)(x^2+x+1)]^2
= (x^3 - 1^3)^2
= (x^3 - 1)^2
= x^6 - 2x^3 + 1

8. (x-2)(x+2)(x^4+4x^2+16)
= (x^2-4)(x^4+4x^2+16)
= (x^2)^3 - 4^3
= x^6 - 64

1. (a+1)(a^2-a+1)

=a(a^2-a+1)+1(a^2-a+1)-----------------將佢break開

=(a^3-a^2+a)+(a^2-a+1) ----------------乘出來:例a(a+b)+1(a+b)=(a^2+ab)+(a+b)

=a^3-a^2+a+a^2-a+1

=a^3+0+0+1-----------------------a^2+a^2=0,+a-a=0

=a^3+1


2. (x-y)(x^2+xy+y^2)

=x(x^2+xy+y^2)-y(x^2+xy+y^2)

=x^3+x^2(y)+xy^2-x^2(y)-xy^2-y^3------------正負得負:-a(a+b)=-a^2-ab

=x^3+0+0-y^3------------------+x^2(y)-x^2(y)=0,+xy^2-xy^2=0

=x^3-y^3


3.(m+2)(m^2-2m+4)

=m(m^2-2m+4)+2(m^2-2m+4)

=(m^3-2m^2+4m)+(2m^2-4m+8)------------負正得負,例:a(a-b)=a^2-ab

=m^3-2m^2+4m+2m^2-4m+8

=m^3+0+0+8---------------- -2m^2+2m^2=0,+4m-4m=0

=m^3+8

4. (a-2b)(a^2+2ab+4b^2)

=a(a^2+2ab+4b^2)-2b(a^2+2ab+4b^2)

=(a^3+2a^2b+4ab^2)+(-2a^2b-2ab^2+8b^3)

=a^3+2a^2b+4ab^2-2a^2b-2ab^2+8b^3

=a^3+0+0+8b^3

=a^3+8b^3


5. (a^2+b)(a^4-a^2b+b^2)

=(a^6-a^4b+a^2b^2)+(a^4b-a^2b^2+b^3)

=a^6-a^4b+a^2b^2+a^4b-a^2b^2+b^3

=a^6+0+0+b^3

=a^6+b^3

6. (a^2-b^2)(a^4+a^2b^2+b^4)

=(a^6+a^4b^2+a^2b^4)+(-a^4b^2-a^4b^2-a^2b^4)

=a^6+0+0+0

=a^6

7. (x-1)^2(x^2+x+1)^2

=[(x-1)(x^2+x+1)]^2

=[x^3+x^2+x-x^2-x-1]^2

=(x^3-1)^2

=x^5-1


8. (x-2)(x+2)(x^4+4x^2+16)

=(x^2-4)(x^4+4x^2+16)

=x^6+4x^4+16x^2-x^4-16x^2-64

=x^6-64

2007-10-04 17:00:13 補充：
7.answer is= x^6 - 2x^3 + 1