To simplify this expression, we will distribute the terms in the second parentheses to each term in the first parentheses.
First, distribute 1/2y to each term in the first parentheses:
1/2y 1/4y^2 = 1/8y^31/2y yz = 1/2y^2z1/2y * 4z^2 = 2yz^2
Next, distribute -2z to each term in the first parentheses:
-2z 1/4y^2 = -1/2y^2z-2z yz = -2yz^2-2z * 4z^2 = -8z^3
Now, combine the terms:
(1/8y^3 + 1/2y^2z + 2yz^2) + (-1/2y^2z - 2yz^2 - 8z^3)
Simplify by combining like terms:
1/8y^3 - 1/2y^2z + 1/8y^3 - 2yz^2 - 8z^3
2/8y^3 - 1/2y^2z - 2yz^2 - 8z^3
1/4y^3 - 1/2y^2z - 2yz^2 - 8z^3
Therefore, the simplified expression is 1/4y^3 - 1/2y^2z - 2yz^2 - 8z^3.
To simplify this expression, we will distribute the terms in the second parentheses to each term in the first parentheses.
First, distribute 1/2y to each term in the first parentheses:
1/2y 1/4y^2 = 1/8y^3
1/2y yz = 1/2y^2z
1/2y * 4z^2 = 2yz^2
Next, distribute -2z to each term in the first parentheses:
-2z 1/4y^2 = -1/2y^2z
-2z yz = -2yz^2
-2z * 4z^2 = -8z^3
Now, combine the terms:
(1/8y^3 + 1/2y^2z + 2yz^2) + (-1/2y^2z - 2yz^2 - 8z^3)
Simplify by combining like terms:
1/8y^3 - 1/2y^2z + 1/8y^3 - 2yz^2 - 8z^3
2/8y^3 - 1/2y^2z - 2yz^2 - 8z^3
1/4y^3 - 1/2y^2z - 2yz^2 - 8z^3
Therefore, the simplified expression is 1/4y^3 - 1/2y^2z - 2yz^2 - 8z^3.