How to simplify this:
(2x-y)(2x+y)(x+2y)
----------------------------
(2x²+3xy-2y²)(y-2x)
yeah that's a fraction.
can it be simplified more?
thanks
(2x-y)(2x+y)(x+2y)
----------------------------
(2x²+3xy-2y²)(y-2x)
yeah that's a fraction.
can it be simplified more?
thanks
-
(2x-y)(2x+y)(x+2y)
----------------------------
(2x²+3xy-2y²)(y-2x)
(2x-y)(2x+y)(x+2y)
-------------------------------
(2x²+3xy-2y²)(2x-y)(-1)
(2x+y)(x+2y)
-----------------------
(2x²+3xy-2y²)(-1)
(2x+y)(x+2y)
-----------------------
(2x-y)(x+2y)(-1)
(2x+y)
------------
(2x-y)(-1)
(2x+y)
--------- I think that's it ;)
(y-2x)
----------------------------
(2x²+3xy-2y²)(y-2x)
(2x-y)(2x+y)(x+2y)
-------------------------------
(2x²+3xy-2y²)(2x-y)(-1)
(2x+y)(x+2y)
-----------------------
(2x²+3xy-2y²)(-1)
(2x+y)(x+2y)
-----------------------
(2x-y)(x+2y)(-1)
(2x+y)
------------
(2x-y)(-1)
(2x+y)
--------- I think that's it ;)
(y-2x)
-
On the first factor (2x - y), it can also be written as -(y - 2x). This cancels out that (y - 2x) in that denominator.
-(2x + y)(x + 2y)
------------------------
(2x^2+3xy-2y^2)
You can factor that denominator.
(2x - y)(x + 2y)
-(2x + y)(x + 2y)
-----------------------
(2x - y)(x + 2y)
You can cancel out (x + 2y)
-(2x + y)
------------
2x - y
Now just eliminate the parentheses.
-2x - y
---------
2x - y
-(2x + y)(x + 2y)
------------------------
(2x^2+3xy-2y^2)
You can factor that denominator.
(2x - y)(x + 2y)
-(2x + y)(x + 2y)
-----------------------
(2x - y)(x + 2y)
You can cancel out (x + 2y)
-(2x + y)
------------
2x - y
Now just eliminate the parentheses.
-2x - y
---------
2x - y
-
= ([2x - y][2x + y][(x + 2y])/([2x² + 3xy - 2y²][y - 2x])
= ([2x - y][2x + y][x + 2y])/([2y² - 3xy - 2x²][2x - y]) cancel 2x - y
= ([2x+ y][x + 2y])/(2y² - 3xy - 2x²]) factor 2y² - 3xy - 2x²
= ([2x + y][x + 2y])/([x + 2y][2x - y]) cancel x + 2y
= (2x + y)/(2x - y)
Answer: (2x + y)/(2x - y) OR quotient of 1 & 2y/(2x - y)
= ([2x - y][2x + y][x + 2y])/([2y² - 3xy - 2x²][2x - y]) cancel 2x - y
= ([2x+ y][x + 2y])/(2y² - 3xy - 2x²]) factor 2y² - 3xy - 2x²
= ([2x + y][x + 2y])/([x + 2y][2x - y]) cancel x + 2y
= (2x + y)/(2x - y)
Answer: (2x + y)/(2x - y) OR quotient of 1 & 2y/(2x - y)
-
(2x-y)(2x+y)(x+2y)
---------------------------- =
(2x²+3xy-2y²)(y-2x)
= (2x-y)(2x+y)(x+2y) / (2x-y)(x+2y)(y -- 2x)
= (y + 2x) / (y -- 2x) ANSWER
---------------------------- =
(2x²+3xy-2y²)(y-2x)
= (2x-y)(2x+y)(x+2y) / (2x-y)(x+2y)(y -- 2x)
= (y + 2x) / (y -- 2x) ANSWER