melindanelu58

因式分解:
1.將9(六次方)-64寫成標準分解式
答案:7*11*67*103

(9^2)^3 -(2^2)^3
=(9^2-2^2)(9^4+9^2*2^2+2^4)

=(9+2)(9-2)(9^4+9^2*2^2+2^4)

=11*7*[(9^2+2^2)^2-9^2*2^2]
=11*7*[(9^2+2^2+9*2)(9^2+2^2-9*2)]
=11*7*103*67

因式分解下列各式(配平方法)
2.9x(四次方)-7x²y²+y(四次方)
答案:(3x²+xy-y²)(3x²-xy-y²)
(3x^2)^2-7(x^2y^2)+(y^2)^2
=[(3x^2-y^2)^2-x^2y^2]
=(3x^2-y^2+xy)(3x^2-y^2-xy)
=(3x^2+xy-y^2)(3x^2-xy-y^2)

3.a(四次方)+a²b²+b(四次方)
答案:(a²+ab+b²)(a²-ab+b²)

(a^2)^2+a^2b^2+(b^2)^2
=[(a^2+b^2)^2-a^2b^2]
=(a^2+ab+b^2)(a^2-ab+b^2)

因式分解:
4.x(四次方)+4
答案(x²+2x+2)(x²-2x+2)
(x^2)^2+2^2
=[(x^2+2)^2-4x^2]
=(x^2+2x+2)(x^2-2x+2)

5.將7(四次方)+4寫成標準分解式
答案:5*13*37
(7^2)^2+2^2
=[(7^2+2)^2-2*7^2*2]
=(7^2+2+14)(7^2+2-14)
=65*37
=5*13*37

因式分解下列各式:
6.x(三次方)-x²-18
答案:(x-3)(x²+2x+6)
(x^3-27)-x^2+9
=(x^3-3^3)-(x^2-3^2)
=(x-3)(x^2+3x+9)-(x+3)(x-3)
=(x-3)[(x^2+3x+9)-(x+3)]
=(x-3)(x^2+2x+6)

7.x²+5xy+6y²-3x-7y+2
答案:(x+2y-1)(x+3y-2)
(x+2y)(x+3y)-3x-7y+2
=(x+2y-1)(x+3y-2)    大十字交乘