Question
Factor the expression
(x−4)(x+4)(x2+16)
Evaluate
x4−256
Rewrite the expression in exponential form
(x2)2−(25621)2
Use a2−b2=(a−b)(a+b) to factor the expression
(x2−25621)(x2+25621)
Evaluate
More Steps

Evaluate
x2−25621
Calculate
More Steps

Evaluate
−25621
Rewrite in exponential form
−(28)21
Multiply the exponents
−28×21
Multiply the exponents
−24
Evaluate the power
−16
x2−16
(x2−16)(x2+25621)
Evaluate
More Steps

Evaluate
x2+25621
Calculate
More Steps

Evaluate
25621
Rewrite in exponential form
(28)21
Multiply the exponents
28×21
Multiply the exponents
24
Evaluate the power
16
x2+16
(x2−16)(x2+16)
Solution
More Steps

Evaluate
x2−16
Rewrite the expression in exponential form
x2−42
Use a2−b2=(a−b)(a+b) to factor the expression
(x−4)(x+4)
(x−4)(x+4)(x2+16)
Show Solution

Find the roots
x1=−4,x2=4
Evaluate
x4−256
To find the roots of the expression,set the expression equal to 0
x4−256=0
Move the constant to the right-hand side and change its sign
x4=0+256
Removing 0 doesn't change the value,so remove it from the expression
x4=256
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4256
Simplify the expression
More Steps

Evaluate
4256
Write the number in exponential form with the base of 4
444
Reduce the index of the radical and exponent with 4
4
x=±4
Separate the equation into 2 possible cases
x=4x=−4
Solution
x1=−4,x2=4
Show Solution
