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

Find the roots
x1=−3,x2=3
Evaluate
x4−81
To find the roots of the expression,set the expression equal to 0
x4−81=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
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
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