請計下列各式

因式分解下列各式(P.S.^=次方)
1)2x^3-3y+2x-3x^2y
=2x(x^2+1)-3y(1+x^2)
=(2x-3y)(x^2+1)

2)a+b+ac+bc
=(a+b)+c(a+b)
=(1+c)(a+b)

3)ab-3a-3b+9
=b(a-3)-3(a-3)
=(b-3)(a-3)

4)6s+6t+sw+tw
=6(s+t)+w(s+t)
=(6+w)(s+t)

5)2ax+3ay-5az-4x-6y+10z
=a(2x+3y-5z)-2(2x+3y-5z)
=(a-2)(2x+3y-5z)

6)xy+x+y+1
=x(y+1)+(y+1)
=(x+1)(y+1)

7)4ax+6ay-6bx-9by
=2a(2x+3y)-3b(2x+3y)
=(2a-3b)(2x+3y)

8)2x^3-3y+2x-3x^2y
=2x(x^2+1)-3y(1+x^2)
=(2x-3y)(x^2+1)

9)ux+2xv+u+2v
=u(x+1)+2v(x+1)
=(u+2v)(x+1)

10) ns-s-mn+m
=s(n-1)-m(n-1)
=(s-m)(n-1)

11) x-2-xy+2y
=x(1-y)-2(1-y)
=(x-2)(1-y)

12)y^3-1-y^2+y
=y(y^2+1)-(y^2-1)
=(y-1)(y^2-1)
=(y-1)(y+1)(y-1)

13) 3b-3c+ab-ac
=3(b-c)+a(b-c)
=(3+a)(b-c)

兩平方之差
利用平方差公式:(a+b)(a-b)=a^2-b^2

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

2 (3+x)(3-x)
=9-x^2

3 (-8+y)(-8-y)
=62-x^2

4 (4y+3)(4y-3)
=16y^2-9

5 (2x^2+7)(2x^2-7)
=4x^4-49

6 (2p+5p)(2p-5p)
=4p^2-25p^2
=-21p^2

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

8 (b-12)(b+12)
=b^2-144

9 (-k-6)(-k+6)
=k^2-36

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

功課自己做啦