EASY MATH

1. (x^3y)^2/y^5=     (x^3y)(x^3y)/y^5=    (x^3)(x^3)(y)(y)/y^5=     (x^6)(y^2)/y^5=     x^6/y^3
2. 4x^2-4xy+y^2=   4x^2 -2xy -2xy +y^2 (Note: -4xy = -2xy – 2xy)=    2x(2x –y) – y(2x–y) =   (2x – y) (2x – y)=    (2x-y)^2
3. 4x^2-4xy+y^2-2x+y=     (2x – y) (2x – y) -2x + y  (Note: factorize (4x^2 -4xy +y^2) first)=    (2x – y) (2x – y)– (2x – y)=   (2x – y) (2x – y)– 1(2x – y)  [Note: (2x –1) is the same as 1(2x -1)]=   (2x – y) [(2x –y)– 1]= (2x - y) (2x –y -1)
4.-3x+1/4 > x - 5     -3x +1/4 + 3x > x – 5 + 3x  (Both sides add 3x)  +1/4 > 4x – 5  +1/4 + 5 > 4x –5 + 5  (Both sides add 5)   5.25 >  4x       5.25/4  >  4x/4  (Both sides are divided by 4)    1.3125  >  x  ( 1.3125 greater than x)   x  <  1.3125

2. 4x^2-4xy+y^2

= (2x-y)^2

3. 4x^2-4xy+y^2-2x+y
= (2x-y)^2-2x+y
= (2x-y)^2-(2x-y)
= (2x-y)(2x-y-1)

4.-3x+1/4>x-5
5.25> 4x
x< 1.3125

第一題至第三題是因式分解，第四題是解不等式，對否？