Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(r−1)(r2+r+1)(r+1)(r2−r+1)
Evaluate
r6−1
Rewrite the expression in exponential form
(r3)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(r3−1)(r3+1)
Evaluate
More Steps
Evaluate
r3−1
Rewrite the expression in exponential form
r3−13
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(r−1)(r2+r×1+12)
Any expression multiplied by 1 remains the same
(r−1)(r2+r+12)
1 raised to any power equals to 1
(r−1)(r2+r+1)
(r−1)(r2+r+1)(r3+1)
Solution
More Steps
Evaluate
r3+1
Rewrite the expression in exponential form
r3+13
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(r+1)(r2−r×1+12)
Any expression multiplied by 1 remains the same
(r+1)(r2−r+12)
1 raised to any power equals to 1
(r+1)(r2−r+1)
(r−1)(r2+r+1)(r+1)(r2−r+1)
Show Solution
Find the roots
r1=−1,r2=1
Evaluate
r6−1
To find the roots of the expression,set the expression equal to 0
r6−1=0
Move the constant to the right-hand side and change its sign
r6=0+1
Removing 0 doesn't change the value,so remove it from the expression
r6=1
Take the root of both sides of the equation and remember to use both positive and negative roots
r=±61
Simplify the expression
r=±1
Separate the equation into 2 possible cases
r=1r=−1
Solution
r1=−1,r2=1
Show Solution