Question
Factor the expression
(3−x)(3+x)(9+x2)
Evaluate
81−x4
Rewrite the expression in exponential form
(8121)2−(x2)2
Use a2−b2=(a−b)(a+b) to factor the expression
(8121−x2)(8121+x2)
Evaluate
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Evaluate
8121−x2
Calculate
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Evaluate
8121
Rewrite in exponential form
(34)21
Multiply the exponents
34×21
Multiply the exponents
32
Evaluate the power
9
9−x2
(9−x2)(8121+x2)
Evaluate
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Evaluate
8121+x2
Calculate
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Evaluate
8121
Rewrite in exponential form
(34)21
Multiply the exponents
34×21
Multiply the exponents
32
Evaluate the power
9
9+x2
(9−x2)(9+x2)
Solution
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Evaluate
9−x2
Rewrite the expression in exponential form
32−x2
Use a2−b2=(a−b)(a+b) to factor the expression
(3−x)(3+x)
(3−x)(3+x)(9+x2)
Show Solution

Find the roots
x1=−3,x2=3
Evaluate
81−x4
To find the roots of the expression,set the expression equal to 0
81−x4=0
Move the constant to the right-hand side and change its sign
−x4=0−81
Removing 0 doesn't change the value,so remove it from the expression
−x4=−81
Change the signs on both sides of the equation
x4=81
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±481
Simplify the expression
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Evaluate
481
Write the number in exponential form with the base of 3
434
Reduce the index of the radical and exponent with 4
3
x=±3
Separate the equation into 2 possible cases
x=3x=−3
Solution
x1=−3,x2=3
Show Solution
