Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x6−x3
Evaluate
x6−x3×1
Solution
x6−x3
Show Solution
Factor the expression
x3(x−1)(x2+x+1)
Evaluate
x6−x3×1
Any expression multiplied by 1 remains the same
x6−x3
Rewrite the expression
x3×x3−x3
Factor out x3 from the expression
x3(x3−1)
Solution
More Steps
Evaluate
x3−1
Calculate
x3+x2+x−x2−x−1
Rewrite the expression
x×x2+x×x+x−x2−x−1
Factor out x from the expression
x(x2+x+1)−x2−x−1
Factor out −1 from the expression
x(x2+x+1)−(x2+x+1)
Factor out x2+x+1 from the expression
(x−1)(x2+x+1)
x3(x−1)(x2+x+1)
Show Solution
Find the roots
x1=0,x2=1
Evaluate
(x6−x3×1)
To find the roots of the expression,set the expression equal to 0
x6−x3×1=0
Any expression multiplied by 1 remains the same
x6−x3=0
Factor the expression
x3(x3−1)=0
Separate the equation into 2 possible cases
x3=0x3−1=0
The only way a power can be 0 is when the base equals 0
x=0x3−1=0
Solve the equation
More Steps
Evaluate
x3−1=0
Move the constant to the right-hand side and change its sign
x3=0+1
Removing 0 doesn't change the value,so remove it from the expression
x3=1
Take the 3-th root on both sides of the equation
3x3=31
Calculate
x=31
Simplify the root
x=1
x=0x=1
Solution
x1=0,x2=1
Show Solution