Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x6−1
Evaluate
x5×x−1
Solution
More Steps
Evaluate
x5×x
Use the product rule an×am=an+m to simplify the expression
x5+1
Add the numbers
x6
x6−1
Show Solution
Factor the expression
(x−1)(x2+x+1)(x+1)(x2−x+1)
Evaluate
x5×x−1
Evaluate
More Steps
Evaluate
x5×x
Use the product rule an×am=an+m to simplify the expression
x5+1
Add the numbers
x6
x6−1
Rewrite the expression in exponential form
(x3)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(x3−1)(x3+1)
Evaluate
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Evaluate
x3−1
Rewrite the expression in exponential form
x3−13
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(x−1)(x2+x×1+12)
Any expression multiplied by 1 remains the same
(x−1)(x2+x+12)
1 raised to any power equals to 1
(x−1)(x2+x+1)
(x−1)(x2+x+1)(x3+1)
Solution
More Steps
Evaluate
x3+1
Rewrite the expression in exponential form
x3+13
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(x+1)(x2−x×1+12)
Any expression multiplied by 1 remains the same
(x+1)(x2−x+12)
1 raised to any power equals to 1
(x+1)(x2−x+1)
(x−1)(x2+x+1)(x+1)(x2−x+1)
Show Solution
Find the roots
x1=−1,x2=1
Evaluate
x5×x−1
To find the roots of the expression,set the expression equal to 0
x5×x−1=0
Multiply the terms
More Steps
Evaluate
x5×x
Use the product rule an×am=an+m to simplify the expression
x5+1
Add the numbers
x6
x6−1=0
Move the constant to the right-hand side and change its sign
x6=0+1
Removing 0 doesn't change the value,so remove it from the expression
x6=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±61
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
Solution
x1=−1,x2=1
Show Solution