Question
Factor the expression
(x−5)(x+5)(x2+25)
Evaluate
x4−625
Rewrite the expression in exponential form
(x2)2−(62521)2
Use a2−b2=(a−b)(a+b) to factor the expression
(x2−62521)(x2+62521)
Evaluate
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Evaluate
x2−62521
Calculate
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Evaluate
−62521
Rewrite in exponential form
−(54)21
Multiply the exponents
−54×21
Multiply the exponents
−52
Evaluate the power
−25
x2−25
(x2−25)(x2+62521)
Evaluate
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Evaluate
x2+62521
Calculate
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Evaluate
62521
Rewrite in exponential form
(54)21
Multiply the exponents
54×21
Multiply the exponents
52
Evaluate the power
25
x2+25
(x2−25)(x2+25)
Solution
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Evaluate
x2−25
Rewrite the expression in exponential form
x2−52
Use a2−b2=(a−b)(a+b) to factor the expression
(x−5)(x+5)
(x−5)(x+5)(x2+25)
Show Solution

Find the roots
x1=−5,x2=5
Evaluate
x4−625
To find the roots of the expression,set the expression equal to 0
x4−625=0
Move the constant to the right-hand side and change its sign
x4=0+625
Removing 0 doesn't change the value,so remove it from the expression
x4=625
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4625
Simplify the expression
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Evaluate
4625
Write the number in exponential form with the base of 5
454
Reduce the index of the radical and exponent with 4
5
x=±5
Separate the equation into 2 possible cases
x=5x=−5
Solution
x1=−5,x2=5
Show Solution
