Question
Simplify the expression
x6−9x5+27x4−27x3
Evaluate
(x×1)3(x−3)3
Any expression multiplied by 1 remains the same
x3(x−3)3
Expand the expression
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Evaluate
(x−3)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
x3−3x2×3+3x×32−33
Calculate
x3−9x2+27x−27
x3(x3−9x2+27x−27)
Apply the distributive property
x3×x3−x3×9x2+x3×27x−x3×27
Multiply the terms
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Evaluate
x3×x3
Use the product rule an×am=an+m to simplify the expression
x3+3
Add the numbers
x6
x6−x3×9x2+x3×27x−x3×27
Multiply the terms
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Evaluate
x3×9x2
Use the commutative property to reorder the terms
9x3×x2
Multiply the terms
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Evaluate
x3×x2
Use the product rule an×am=an+m to simplify the expression
x3+2
Add the numbers
x5
9x5
x6−9x5+x3×27x−x3×27
Multiply the terms
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Evaluate
x3×27x
Use the commutative property to reorder the terms
27x3×x
Multiply the terms
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Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
27x4
x6−9x5+27x4−x3×27
Solution
x6−9x5+27x4−27x3
Show Solution

Find the roots
x1=0,x2=3
Evaluate
(x×1)3(x−3)3
To find the roots of the expression,set the expression equal to 0
(x×1)3(x−3)3=0
Any expression multiplied by 1 remains the same
x3(x−3)3=0
Separate the equation into 2 possible cases
x3=0(x−3)3=0
The only way a power can be 0 is when the base equals 0
x=0(x−3)3=0
Solve the equation
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Evaluate
(x−3)3=0
The only way a power can be 0 is when the base equals 0
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=0x=3
Solution
x1=0,x2=3
Show Solution
