因式分解~求救

1.) A=1/2 r^2=>r=√(2A)

2.) c^2 = a^2 + b^2=>b^2=√(c^2-a^2)

3.) f= 1/2 L √T/m=>T=(2fm/L)^2

因式分解

4.) 2a^2c - 6a^2d +7c - 21d
=2a^2(c-3d)+7(c-3d)
=(2a^2+7)(c-3d)

5.) -12y^2 + 36xy -27x^2
=-3(9x^2-12xy+4y^2)
=-3(3x-2y)^2

6.)2-18y^2
=2-2(3y)^2
=2[1-(3y)^2]
=2(1+3y)(1-3y)

7.)49-(3x-2)^2
=(7+3x-2)(7-3x+2)
=(3x+5)(9-3x)

8.) (2x+1)^2 -(3x-2)^2
=(2x+1+3x-2)(2x+1-3x+2)
=(5x-1)(3-x)

9.) 144(2x+y)^2 - 25(3x- 2y)^2
=[12(2x+y)+5(3x-2y)][12(2x+y)-5(3x-2y)]
=(24x+12y+15x-10y)(24x+12y-15x+10y)
=(39x+2y)(9x+22y)

把括號內的字母變换成公的主頂

1.) A=1/2 r^2
2A=r^2
r^2=2A
r=開方(2A)

2.) c^2 = a^2 + b^2
b^2=c^2-a^2
b=開方(c^a-a^2)
(T)
3.) f= 1/2 L √T/m[係咪開方(T/m)]
2f/L=開方(T/m)
(2f/L)^2=T/m
T/m=(2f/L)^2
T/m=4f^2/L^2
T=m(4f^2/L^2)
T=(4mf^2)/L^2


因式分解

4.) 2a^2c - 6a^2d +7c - 21d
= 2a^2c+7c-6a^2d-21d
= c(2a^2+7)-3d(2a^2+7)
=(c-3d)(2a^2+7)

5.) -12y^2 + 36xy -27x^2
= -(12y^2-36xy+27x^2)
=-(6y-9x)(2y-3x)

6.)2-18y^2
=2(1-9y^2)
=2(1+3y)(1-3y)

7.)49-(3x-2)^2
=7^2-(3x-3)^2
=(7+3x-3)(7-3x+3)

8.) (2x+1)^2 -(3x-2)^2
=(2x+1+3x-2)(2x+1-3x+2)
=(5x-1)(3-x)

9.) 144(2x+y)^2 - 25(3x- 2y)^2
=[12(2x+y)]^2-[5(3x-2y)]^2
=(24x+12y)^2-(15x-10y)^2
=(24x+12y+15x-10y)(24x+12y-15x+10y)
=(39x+2y)(9x+22y)