Question
Simplify the expression
x5−3x4+3x3−x2
Evaluate
(x−1)(x−1)(x−1)x2
Rewrite the expression in exponential form
(x−1)3x2
Use the commutative property to reorder the terms
x2(x−1)3
Expand the expression
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Evaluate
(x−1)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
x3−3x2×1+3x×12−13
Calculate
x3−3x2+3x−1
x2(x3−3x2+3x−1)
Apply the distributive property
x2×x3−x2×3x2+x2×3x−x2×1
Multiply the terms
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Evaluate
x2×x3
Use the product rule an×am=an+m to simplify the expression
x2+3
Add the numbers
x5
x5−x2×3x2+x2×3x−x2×1
Multiply the terms
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Evaluate
x2×3x2
Use the commutative property to reorder the terms
3x2×x2
Multiply the terms
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Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
3x4
x5−3x4+x2×3x−x2×1
Multiply the terms
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Evaluate
x2×3x
Use the commutative property to reorder the terms
3x2×x
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
3x3
x5−3x4+3x3−x2×1
Solution
x5−3x4+3x3−x2
Show Solution

Find the roots
x1=0,x2=1
Evaluate
(x−1)(x−1)(x−1)(x2)
To find the roots of the expression,set the expression equal to 0
(x−1)(x−1)(x−1)(x2)=0
Calculate
(x−1)(x−1)(x−1)x2=0
Multiply
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Multiply the terms
(x−1)(x−1)(x−1)x2
Multiply the terms with the same base by adding their exponents
(x−1)1+1+1x2
Add the numbers
(x−1)3x2
Use the commutative property to reorder the terms
x2(x−1)3
x2(x−1)3=0
Separate the equation into 2 possible cases
x2=0(x−1)3=0
The only way a power can be 0 is when the base equals 0
x=0(x−1)3=0
Solve the equation
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Evaluate
(x−1)3=0
The only way a power can be 0 is when the base equals 0
x−1=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
x=0x=1
Solution
x1=0,x2=1
Show Solution
