Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x3−x6
Evaluate
(1−x×x2)(1×x×x2)
Remove the parentheses
(1−x×x2)×1×x×x2
Multiply the terms
More Steps
Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
(1−x3)×1×x×x2
Rewrite the expression
(1−x3)x×x2
Multiply the terms with the same base by adding their exponents
(1−x3)x1+2
Add the numbers
(1−x3)x3
Multiply the terms
x3(1−x3)
Apply the distributive property
x3×1−x3×x3
Any expression multiplied by 1 remains the same
x3−x3×x3
Solution
More Steps
Evaluate
x3×x3
Use the product rule an×am=an+m to simplify the expression
x3+3
Add the numbers
x6
x3−x6
Show Solution
Factor the expression
x3(1−x)(x2+x+1)
Evaluate
(1−x×x2)(1×x×x2)
Remove the parentheses
(1−x×x2)×1×x×x2
Multiply the terms
More Steps
Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
(1−x3)×1×x×x2
Multiply the terms
More Steps
Multiply the terms
1×x×x2
Rewrite the expression
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
(1−x3)x3
Multiply the terms
x3(1−x3)
Solution
More Steps
Evaluate
1−x3
Calculate
x2+x+1−x3−x2−x
Rewrite the expression
x2+x+1−x×x2−x×x−x
Factor out −x from the expression
x2+x+1−x(x2+x+1)
Factor out x2+x+1 from the expression
(1−x)(x2+x+1)
x3(1−x)(x2+x+1)
Show Solution
Find the roots
x1=0,x2=1
Evaluate
(1−x×x2)(1×x×x2)
To find the roots of the expression,set the expression equal to 0
(1−x×x2)(1×x×x2)=0
Multiply the terms
More Steps
Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
(1−x3)(1×x×x2)=0
Multiply the terms
More Steps
Multiply the terms
1×x×x2
Rewrite the expression
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
(1−x3)x3=0
Multiply the terms
x3(1−x3)=0
Separate the equation into 2 possible cases
x3=01−x3=0
The only way a power can be 0 is when the base equals 0
x=01−x3=0
Solve the equation
More Steps
Evaluate
1−x3=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
Change the signs on both sides of the equation
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