Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
n2(n−2)(n+2)
Evaluate
n4−4n2
Factor out n2 from the expression
n2(n2−4)
Solution
More Steps
Evaluate
n2−4
Rewrite the expression in exponential form
n2−22
Use a2−b2=(a−b)(a+b) to factor the expression
(n−2)(n+2)
n2(n−2)(n+2)
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Find the roots
n1=−2,n2=0,n3=2
Evaluate
n4−4n2
To find the roots of the expression,set the expression equal to 0
n4−4n2=0
Factor the expression
n2(n2−4)=0
Separate the equation into 2 possible cases
n2=0n2−4=0
The only way a power can be 0 is when the base equals 0
n=0n2−4=0
Solve the equation
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Evaluate
n2−4=0
Move the constant to the right-hand side and change its sign
n2=0+4
Removing 0 doesn't change the value,so remove it from the expression
n2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±4
Simplify the expression
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Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
n=±2
Separate the equation into 2 possible cases
n=2n=−2
n=0n=2n=−2
Solution
n1=−2,n2=0,n3=2
Show Solution