How do you simplify?
(2-y)(1/2y^2-(1/4y^4 - 1/2y^2))
=(2+-y) (1/2y^2 + -1/4y^4+1/2y^2)
=(2) (1/2y^2) + (2) (-1/4y^4) + (2) (1/2y^2) + (-y) (1/2y^2) + (-y) (-1/4y^4) + (-y) (1/2y^2)
Think you got the rest?
(1/2y^2-(1/4y^4 - 1/2y^2))
= -1/4 y^4 + y^2
= -1/4 y^2 (y^2-4)
Now multiply that by 2-y and you have
1/4 y^2 (y-2)^2 (y+2)
Not sure where you want to go with that
To simplify the given expression (2-y)(1/2y^2-(1/4y^4 - 1/2y^2)), you can follow these steps:
Step 1: Remove the parentheses using the distributive property.
(2-y)(1/2y^2) - (2-y)(1/4y^4 - 1/2y^2)
Step 2: Apply the distributive property to each term.
(2 * 1/2y^2 - y * 1/2y^2) - (2 * 1/4y^4 - 2 * 1/2y^2 - y * 1/4y^4 + y * 1/2y^2)
Simplified expression: 1/y^2 - y/2 - 1/2y^2 + 1/4y^4 - y/2 + 1/4y^4 - y^2/4 + y^3/2
Step 3: Combine like terms.
To combine the terms, we need to have the same exponent for each variable term:
1/y^2 - 1/2y^2 - y/2 - y/2 + 1/4y^4 + 1/4y^4 - y^2/4 + y^3/2
Now, let's combine the like terms:
(1/4y^4 + 1/4y^4) = 1/2y^4
(- y/2 - y/2) = - y
(- y/2 - y/2) = - y
(1/y^2 - 1/2y^2) = - 1/2y^2
(- y^2/4) = - y^2/4
(y^3/2) = y^3/2
Simplified expression: 1/2y^4 - y - y - 1/2y^2 - y^2/4 + y^3/2
Final Answer: 1/2y^4 - 2y - 1/2y^2 - y^2/4 + y^3/2
Following these steps, you can simplify the given expression.