Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x2−2x3+x4
Evaluate
(x×1−x2)2
Any expression multiplied by 1 remains the same
(x−x2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×x2+(x2)2
Solution
x2−2x3+x4
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Factor the expression
x2(1−x)2
Evaluate
(x×1−x2)2
Any expression multiplied by 1 remains the same
(x−x2)2
Factor the expression
More Steps
Evaluate
x−x2
Rewrite the expression
x−x×x
Factor out x from the expression
x(1−x)
(x(1−x))2
Solution
x2(1−x)2
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Find the roots
x1=0,x2=1
Evaluate
(x×1−x2)2
To find the roots of the expression,set the expression equal to 0
(x×1−x2)2=0
Any expression multiplied by 1 remains the same
(x−x2)2=0
The only way a power can be 0 is when the base equals 0
x−x2=0
Factor the expression
More Steps
Evaluate
x−x2
Rewrite the expression
x−x×x
Factor out x from the expression
x(1−x)
x(1−x)=0
When the product of factors equals 0,at least one factor is 0
x=01−x=0
Solve the equation for x
More Steps
Evaluate
1−x=0
Move the constant to the right-hand side and change its sign
−x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−x=−1
Change the signs on both sides of the equation
x=1
x=0x=1
Solution
x1=0,x2=1
Show Solution