Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x8−1
Evaluate
(x4)2−1
Multiply the exponents
x4×2−1
Solution
x8−1
Show Solution
Factor the expression
(x−1)(x+1)(x2+1)(x4+1)
Evaluate
(x4)2−1
Evaluate
More Steps
Evaluate
(x4)2
Multiply the exponents
x4×2
Multiply the numbers
x8
x8−1
Rewrite the expression in exponential form
(x4)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(x4−1)(x4+1)
Solution
More Steps
Evaluate
x4−1
Rewrite the expression in exponential form
(x2)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(x2−1)(x2+1)
Evaluate
More Steps
Evaluate
x2−1
Rewrite the expression in exponential form
x2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(x−1)(x+1)
(x−1)(x+1)(x2+1)
(x−1)(x+1)(x2+1)(x4+1)
Show Solution
Find the roots
x1=−1,x2=1
Evaluate
(x4)2−1
To find the roots of the expression,set the expression equal to 0
(x4)2−1=0
Evaluate the power
More Steps
Evaluate
(x4)2
Transform the expression
x4×2
Multiply the numbers
x8
x8−1=0
Move the constant to the right-hand side and change its sign
x8=0+1
Removing 0 doesn't change the value,so remove it from the expression
x8=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±81
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
Solution
x1=−1,x2=1
Show Solution