Question
Simplify the expression
x7−3x6+3x5−x4
Evaluate
(x−1)3(x×1)4
Any expression multiplied by 1 remains the same
(x−1)3x4
Use the commutative property to reorder the terms
x4(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
x4(x3−3x2+3x−1)
Apply the distributive property
x4×x3−x4×3x2+x4×3x−x4×1
Multiply the terms
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Evaluate
x4×x3
Use the product rule an×am=an+m to simplify the expression
x4+3
Add the numbers
x7
x7−x4×3x2+x4×3x−x4×1
Multiply the terms
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Evaluate
x4×3x2
Use the commutative property to reorder the terms
3x4×x2
Multiply the terms
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Evaluate
x4×x2
Use the product rule an×am=an+m to simplify the expression
x4+2
Add the numbers
x6
3x6
x7−3x6+x4×3x−x4×1
Multiply the terms
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Evaluate
x4×3x
Use the commutative property to reorder the terms
3x4×x
Multiply the terms
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Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
3x5
x7−3x6+3x5−x4×1
Solution
x7−3x6+3x5−x4
Show Solution

Find the roots
x1=0,x2=1
Evaluate
(x−1)3(x×1)4
To find the roots of the expression,set the expression equal to 0
(x−1)3(x×1)4=0
Any expression multiplied by 1 remains the same
(x−1)3x4=0
Use the commutative property to reorder the terms
x4(x−1)3=0
Separate the equation into 2 possible cases
x4=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
