Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(w−1)(w2+w+1)(w+1)(w2−w+1)
Evaluate
w6−1
Rewrite the expression in exponential form
(w3)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(w3−1)(w3+1)
Evaluate
More Steps
Evaluate
w3−1
Rewrite the expression in exponential form
w3−13
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(w−1)(w2+w×1+12)
Any expression multiplied by 1 remains the same
(w−1)(w2+w+12)
1 raised to any power equals to 1
(w−1)(w2+w+1)
(w−1)(w2+w+1)(w3+1)
Solution
More Steps
Evaluate
w3+1
Rewrite the expression in exponential form
w3+13
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(w+1)(w2−w×1+12)
Any expression multiplied by 1 remains the same
(w+1)(w2−w+12)
1 raised to any power equals to 1
(w+1)(w2−w+1)
(w−1)(w2+w+1)(w+1)(w2−w+1)
Show Solution
Find the roots
w1=−1,w2=1
Evaluate
w6−1
To find the roots of the expression,set the expression equal to 0
w6−1=0
Move the constant to the right-hand side and change its sign
w6=0+1
Removing 0 doesn't change the value,so remove it from the expression
w6=1
Take the root of both sides of the equation and remember to use both positive and negative roots
w=±61
Simplify the expression
w=±1
Separate the equation into 2 possible cases
w=1w=−1
Solution
w1=−1,w2=1
Show Solution