Maths Help F.2

1. 6(r-1)2+8(r-1)
=2(r-1)[3(r+1)+4]
=2(r-1)(3r+3+4)
=2(r-1)(3r+7)
2. 12(p+q)r2-16(p+q)r
=4(p+q)(3r-4)r
3.9(a+b)2y-159(a+b)y2
=3(a+b)y[3(a+b)-53y]
=3(a+b)y(3a+3b-53y)
4.a-b+ac-bc
=(a-b)+c(a-b)
=(a-b)(1+c)
5.xy+xz+6y+6z
=x(y+z)+6(y+z)
=(x+6)(y+z)
6.6ac-bd-6ad+bc
=6ac-6ad+bc-bd
=6a(c-d)+b(c-d)
=(6a+b)(c-d)
7.(3a-2)2-9(3a-3)2
=[(3a-2)-3(3a-3)][(3a-2)+3(3a-3)]
=(7-6a)(12a-11)
8.81(x-y)2-64(2x+1)2
=[9(x-y)-8(2x+1)][9(x-y)+8(2x+1)]
=(9x-9y-16x-8)(9x-9y+16x+8)
=(-25x-9y-8)(25-9y+8)
=-(25x+9y+8)(25-9y+8)

1. 6(r-1)^2+8(r-1)
= [2(r-1)][3(r-1)+4]
= (2r-2)(3r+1)
2. 12(p+q)r^2-16(p+q)r
= [4(p+q)r](3r-4)
= 4p(p+q)(3r-4)
3. 9(a+b)^2y-159a+b)y^2
數式不完整
估計: 9(a+b)^2y-15(a+b)y^2
= [3(a+b)y][3(a+b)-5y]
= 3y(a+b)(3a+3b-5y)
4. a-b+ac-bc
= (a-b)+c(a-b)
= (1+c)(a-b)
5. xy+xz+6y+6z
= x(y+z)+6(y+z)
= (x+6)(y+z)
6. 6ac-bd-6ad+bc
= 6ac-6ad+bc-bd
= 6a(c-d)+b(c-d)
= (6a+b)(c-d)
7. (3a-2)^2-93a-3)^2
數式不完整
估計: (3a-2)^2-(3a-3)^2
= [(3a-2)+(3a-3)][(3a-2)-(3a-3)]
= (6a-5)(1)
= 6a-5
8. 81(x-y)^2-64(2x+1)^2
= [9(x-y)]^2-[8(2x+1)]^2
= {[9(x-y)]+[8(2x+1)]}{[9(x-y)]-[8(2x+1)]}
= [9x-9y+16x+8][9x-9y-16x-8]
= (25x-9y+3)(-7x-9y-8)