Perform the multiplication and simplify and get the restrictions.
(y^3 - 8) / (2y^3) * (4y) / (y^2-11y+18)
hello, why no response
(y^3 - 8) / (2y^3) * (4y) / (y^2-11y+18)
= (y-2)(y^2+2y+4)/(2y^3) * (4y)/((y-2)(y-9))
The denominator cannot be zero, so y≠0,2,9
Now 2y and y-2 cancel, so
(2(y^2+2y+4))/(y^2(y-9))
To perform the multiplication and simplify the expression, follow these steps:
Step 1: Multiply the numerators together: (y^3 - 8) * (4y)
The result is: 4y(y^3 - 8) = 4y^4 - 32y
Step 2: Multiply the denominators together: (2y^3) * (y^2-11y+18)
The result is: 2y^3(y^2 - 11y + 18) = 2y^5 - 22y^4 + 36y^3
Step 3: Simplify the expression by canceling out any common factors between the numerator and denominator.
The simplified expression is: (4y^4 - 32y) / (2y^5 - 22y^4 + 36y^3)
To find the restrictions of the expression, look for any values of y that would result in dividing by zero. In this case, we need to find values of y that make the denominator equal to zero.
Step 4: Set the denominator equal to zero and solve for y:
2y^5 - 22y^4 + 36y^3 = 0
Factor out the common term of y^3:
y^3(2y^2 - 22y + 36) = 0
Now, set each factor equal to zero and solve for y:
1. y^3 = 0
y = 0
2. 2y^2 - 22y + 36 = 0
Solve this quadratic equation using the quadratic formula or factoring methods.
By identifying the roots, you can determine the restrictions on the original expression. In this case, the restrictions are that y cannot be equal to 0 and cannot satisfy the solutions obtained from the quadratic equation.