Question
Simplify the expression
u23u−4u43u
Evaluate
(u2−4u4)u31
Multiply the terms
u31(u2−4u4)
Use anm=nam to transform the expression
3u×(u2−4u4)
Multiply each term in the parentheses by 3u
3u×u2+3u×(−4u4)
Calculate the product
u23u+3u×(−4u4)
Solution
u23u−4u43u
Show Solution
Factor the expression
u23u×(1−2u)(1+2u)
Evaluate
(u2−4u4)u31
Multiply the terms
u31(u2−4u4)
Use anm=nam to transform the expression
3u×(u2−4u4)
Multiply each term in the parentheses by 3u
3u×u2+3u×(−4u4)
Calculate the product
u23u+3u×(−4u4)
Calculate the product
u23u−4u43u
Rewrite the expression
u23u−u23u×4u2
Factor out u23u from the expression
u23u×(1−4u2)
Solution
u23u×(1−2u)(1+2u)
Show Solution
Find the roots
u1=−21,u2=0,u3=21
Alternative Form
u1=−0.5,u2=0,u3=0.5
Evaluate
(u2−4u4)u31
To find the roots of the expression,set the expression equal to 0
(u2−4u4)u31=0
Multiply the terms
u31(u2−4u4)=0
Separate the equation into 2 possible cases
u31=0u2−4u4=0
The only way a power can be 0 is when the base equals 0
u=0u2−4u4=0
Solve the equation
More Steps
Evaluate
u2−4u4=0
Factor the expression
u2(1−4u2)=0
Separate the equation into 2 possible cases
u2=01−4u2=0
The only way a power can be 0 is when the base equals 0
u=01−4u2=0
Solve the equation
More Steps
Evaluate
1−4u2=0
Move the constant to the right-hand side and change its sign
−4u2=0−1
Removing 0 doesn't change the value,so remove it from the expression
−4u2=−1
Change the signs on both sides of the equation
4u2=1
Divide both sides
44u2=41
Divide the numbers
u2=41
Take the root of both sides of the equation and remember to use both positive and negative roots
u=±41
Simplify the expression
u=±21
Separate the equation into 2 possible cases
u=21u=−21
u=0u=21u=−21
u=0u=0u=21u=−21
Find the union
u=0u=21u=−21
Solution
u1=−21,u2=0,u3=21
Alternative Form
u1=−0.5,u2=0,u3=0.5
Show Solution