Question
Factor the expression
(2−n)(2+n)(4+n2)
Evaluate
16−n4
Rewrite the expression in exponential form
(1621)2−(n2)2
Use a2−b2=(a−b)(a+b) to factor the expression
(1621−n2)(1621+n2)
Evaluate
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Evaluate
1621−n2
Calculate
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Evaluate
1621
Rewrite in exponential form
(24)21
Multiply the exponents
24×21
Multiply the exponents
22
Evaluate the power
4
4−n2
(4−n2)(1621+n2)
Evaluate
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Evaluate
1621+n2
Calculate
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Evaluate
1621
Rewrite in exponential form
(24)21
Multiply the exponents
24×21
Multiply the exponents
22
Evaluate the power
4
4+n2
(4−n2)(4+n2)
Solution
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Evaluate
4−n2
Rewrite the expression in exponential form
22−n2
Use a2−b2=(a−b)(a+b) to factor the expression
(2−n)(2+n)
(2−n)(2+n)(4+n2)
Show Solution

Find the roots
n1=−2,n2=2
Evaluate
16−n4
To find the roots of the expression,set the expression equal to 0
16−n4=0
Move the constant to the right-hand side and change its sign
−n4=0−16
Removing 0 doesn't change the value,so remove it from the expression
−n4=−16
Change the signs on both sides of the equation
n4=16
Take the root of both sides of the equation and remember to use both positive and negative roots
n=±416
Simplify the expression
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Evaluate
416
Write the number in exponential form with the base of 2
424
Reduce the index of the radical and exponent with 4
2
n=±2
Separate the equation into 2 possible cases
n=2n=−2
Solution
n1=−2,n2=2
Show Solution
