Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
n5−n
Evaluate
n5−n×1
Solution
n5−n
Show Solution
Factor the expression
n(n−1)(n+1)(n2+1)
Evaluate
n5−n×1
Any expression multiplied by 1 remains the same
n5−n
Factor out n from the expression
n(n4−1)
Factor the expression
More Steps
Evaluate
n4−1
Rewrite the expression in exponential form
(n2)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(n2−1)(n2+1)
n(n2−1)(n2+1)
Solution
More Steps
Evaluate
n2−1
Rewrite the expression in exponential form
n2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(n−1)(n+1)
n(n−1)(n+1)(n2+1)
Show Solution
Find the roots
n1=−1,n2=0,n3=1
Evaluate
n5−n×1
To find the roots of the expression,set the expression equal to 0
n5−n×1=0
Any expression multiplied by 1 remains the same
n5−n=0
Factor the expression
n(n4−1)=0
Separate the equation into 2 possible cases
n=0n4−1=0
Solve the equation
More Steps
Evaluate
n4−1=0
Move the constant to the right-hand side and change its sign
n4=0+1
Removing 0 doesn't change the value,so remove it from the expression
n4=1
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±41
Simplify the expression
n=±1
Separate the equation into 2 possible cases
n=1n=−1
n=0n=1n=−1
Solution
n1=−1,n2=0,n3=1
Show Solution