Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
k5−k
Evaluate
(k×1)5−(k×1)
Any expression multiplied by 1 remains the same
k5−(k×1)
Solution
k5−k
Show Solution
Factor the expression
k(k−1)(k+1)(k2+1)
Evaluate
(k×1)5−(k×1)
Any expression multiplied by 1 remains the same
k5−(k×1)
Evaluate
More Steps
Evaluate
(k×1)
Evaluate
k×1
Any expression multiplied by 1 remains the same
k
k5−k
Factor out k from the expression
k(k4−1)
Factor the expression
More Steps
Evaluate
k4−1
Rewrite the expression in exponential form
(k2)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(k2−1)(k2+1)
k(k2−1)(k2+1)
Solution
More Steps
Evaluate
k2−1
Rewrite the expression in exponential form
k2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(k−1)(k+1)
k(k−1)(k+1)(k2+1)
Show Solution
Find the roots
k1=−1,k2=0,k3=1
Evaluate
(k×1)5−(k×1)
To find the roots of the expression,set the expression equal to 0
(k×1)5−(k×1)=0
Any expression multiplied by 1 remains the same
k5−(k×1)=0
Any expression multiplied by 1 remains the same
k5−k=0
Factor the expression
k(k4−1)=0
Separate the equation into 2 possible cases
k=0k4−1=0
Solve the equation
More Steps
Evaluate
k4−1=0
Move the constant to the right-hand side and change its sign
k4=0+1
Removing 0 doesn't change the value,so remove it from the expression
k4=1
Take the root of both sides of the equation and remember to use both positive and negative roots
k=±41
Simplify the expression
k=±1
Separate the equation into 2 possible cases
k=1k=−1
k=0k=1k=−1
Solution
k1=−1,k2=0,k3=1
Show Solution