Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
q−q4
Evaluate
q×1−q4
Solution
q−q4
Show Solution
Factor the expression
q(1−q)(1+q+q2)
Evaluate
q×1−q4
Any expression multiplied by 1 remains the same
q−q4
Factor out q from the expression
q(1−q3)
Solution
More Steps
Evaluate
1−q3
Rewrite the expression in exponential form
13−q3
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(1−q)(12+1×q+q2)
1 raised to any power equals to 1
(1−q)(1+1×q+q2)
Any expression multiplied by 1 remains the same
(1−q)(1+q+q2)
q(1−q)(1+q+q2)
Show Solution
Find the roots
q1=0,q2=1
Evaluate
q×1−q4
To find the roots of the expression,set the expression equal to 0
q×1−q4=0
Any expression multiplied by 1 remains the same
q−q4=0
Factor the expression
q(1−q3)=0
Separate the equation into 2 possible cases
q=01−q3=0
Solve the equation
More Steps
Evaluate
1−q3=0
Move the constant to the right-hand side and change its sign
−q3=0−1
Removing 0 doesn't change the value,so remove it from the expression
−q3=−1
Change the signs on both sides of the equation
q3=1
Take the 3-th root on both sides of the equation
3q3=31
Calculate
q=31
Simplify the root
q=1
q=0q=1
Solution
q1=0,q2=1
Show Solution