Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
n4(1−n)(1+n)
Evaluate
n4−n6
Factor out n4 from the expression
n4(1−n2)
Solution
More Steps
Evaluate
1−n2
Rewrite the expression in exponential form
12−n2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−n)(1+n)
n4(1−n)(1+n)
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Find the roots
n1=−1,n2=0,n3=1
Evaluate
n4−n6
To find the roots of the expression,set the expression equal to 0
n4−n6=0
Factor the expression
n4(1−n2)=0
Separate the equation into 2 possible cases
n4=01−n2=0
The only way a power can be 0 is when the base equals 0
n=01−n2=0
Solve the equation
More Steps
Evaluate
1−n2=0
Move the constant to the right-hand side and change its sign
−n2=0−1
Removing 0 doesn't change the value,so remove it from the expression
−n2=−1
Change the signs on both sides of the equation
n2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±1
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
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