s5 數學問題主項、因式分解(1)

1.
x^2y=ay+b
(x^2 - a)y=b
y=b/(x^2 - a)

2.
a=(b+4)/b
ab=b+4
(a-1)b=4
b=4/(a-1)

3.
(r/s)^3 (s^8/r)
=(r^2)(s^5)

4.
[（a^4) (3√ａ^2)] /a^-2 （條題有D奇怪，根號完之後又平方）

5.
9x^2-4
=(3x)^2-2^2
=(3x+2)(3x-2)

6.
x^2-4x+4
=x^2-4x+2^2
=(x-2)^2

7.
x^2+8a+16
=x^2+8a+4^2
=(x+4)^2

8.
2x^2+7x+3
=(2x+1)(x+3)

9.
r^2+10r+25
=r^2+10r+5^2
=(r+5)^2

10.
r^2+10r+25-s^2
=(r+5)^2-s^2 (by 9 )
=(r+5+s)(r+5-s)
=(r+s+5)(r-s+5)

1.
x^2y=ay+b [y]
x^2y-ay=b
y=b/(x^2-a)

2
a=(b+4)/b [b]
a-1=4/b
b=4(a-1)

3.
(r/s)^3 (s^8/r)
=[(r^3)/(s^3)][(s^8)/r]
=(r^2)(s^5)

4
[（a^4/3) (3√ａ^2)]÷(a^-2)
=(a^4/3)(a^2/3)/(a^-2)
=a^4

5.
9x^2-4
=(3x-2)(3x+2)

6
x^2-4x+4
=(x-2)^2

7.
x^2+8a+16
=(x+4)^2

8.
2x^2+7x+3
=(2x+1)(x+3)

9
r^2+10r+25
=(r+5)^2

10
r^2+10r+25-s^2
=(r+5)^2-s^2
=(r+s+5)(r-s+5)