Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
n3(n−1)(n2+n+1)(n+1)(n2−n+1)
Evaluate
n9−n3
Factor out n3 from the expression
n3(n6−1)
Factor the expression
More Steps
Evaluate
n6−1
Rewrite the expression in exponential form
(n3)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(n3−1)(n3+1)
n3(n3−1)(n3+1)
Evaluate
More Steps
Evaluate
n3−1
Rewrite the expression in exponential form
n3−13
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(n−1)(n2+n×1+12)
Any expression multiplied by 1 remains the same
(n−1)(n2+n+12)
1 raised to any power equals to 1
(n−1)(n2+n+1)
n3(n−1)(n2+n+1)(n3+1)
Solution
More Steps
Evaluate
n3+1
Rewrite the expression in exponential form
n3+13
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(n+1)(n2−n×1+12)
Any expression multiplied by 1 remains the same
(n+1)(n2−n+12)
1 raised to any power equals to 1
(n+1)(n2−n+1)
n3(n−1)(n2+n+1)(n+1)(n2−n+1)
Show Solution
Find the roots
n1=−1,n2=0,n3=1
Evaluate
n9−n3
To find the roots of the expression,set the expression equal to 0
n9−n3=0
Factor the expression
n3(n6−1)=0
Separate the equation into 2 possible cases
n3=0n6−1=0
The only way a power can be 0 is when the base equals 0
n=0n6−1=0
Solve the equation
More Steps
Evaluate
n6−1=0
Move the constant to the right-hand side and change its sign
n6=0+1
Removing 0 doesn't change the value,so remove it from the expression
n6=1
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±61
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