Question
Simplify the expression
x7−6x6+13x5−12x4+4x3
Evaluate
(x−2)(x−1)2(x×1)3(x−2)
Any expression multiplied by 1 remains the same
(x−2)(x−1)2x3(x−2)
Use the commutative property to reorder the terms
(x−2)x3(x−1)2(x−2)
Multiply the terms
(x−2)2x3(x−1)2
Expand the expression
More Steps

Evaluate
(x−2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×2+22
Calculate
x2−4x+4
(x2−4x+4)x3(x−1)2
Expand the expression
More Steps

Evaluate
(x−1)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×1+12
Calculate
x2−2x+1
(x2−4x+4)x3(x2−2x+1)
Multiply the terms
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Evaluate
(x2−4x+4)x3
Apply the distributive property
x2×x3−4x×x3+4x3
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
x5−4x×x3+4x3
Multiply the terms
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Evaluate
x×x3
Use the product rule an×am=an+m to simplify the expression
x1+3
Add the numbers
x4
x5−4x4+4x3
(x5−4x4+4x3)(x2−2x+1)
Apply the distributive property
x5×x2−x5×2x+x5×1−4x4×x2−(−4x4×2x)−4x4×1+4x3×x2−4x3×2x+4x3×1
Multiply the terms
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Evaluate
x5×x2
Use the product rule an×am=an+m to simplify the expression
x5+2
Add the numbers
x7
x7−x5×2x+x5×1−4x4×x2−(−4x4×2x)−4x4×1+4x3×x2−4x3×2x+4x3×1
Multiply the terms
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Evaluate
x5×2x
Use the commutative property to reorder the terms
2x5×x
Multiply the terms
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Evaluate
x5×x
Use the product rule an×am=an+m to simplify the expression
x5+1
Add the numbers
x6
2x6
x7−2x6+x5×1−4x4×x2−(−4x4×2x)−4x4×1+4x3×x2−4x3×2x+4x3×1
Any expression multiplied by 1 remains the same
x7−2x6+x5−4x4×x2−(−4x4×2x)−4x4×1+4x3×x2−4x3×2x+4x3×1
Multiply the terms
More Steps

Evaluate
x4×x2
Use the product rule an×am=an+m to simplify the expression
x4+2
Add the numbers
x6
x7−2x6+x5−4x6−(−4x4×2x)−4x4×1+4x3×x2−4x3×2x+4x3×1
Multiply the terms
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Evaluate
−4x4×2x
Multiply the numbers
−8x4×x
Multiply the terms
More Steps

Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
−8x5
x7−2x6+x5−4x6−(−8x5)−4x4×1+4x3×x2−4x3×2x+4x3×1
Any expression multiplied by 1 remains the same
x7−2x6+x5−4x6−(−8x5)−4x4+4x3×x2−4x3×2x+4x3×1
Multiply the terms
More Steps

Evaluate
x3×x2
Use the product rule an×am=an+m to simplify the expression
x3+2
Add the numbers
x5
x7−2x6+x5−4x6−(−8x5)−4x4+4x5−4x3×2x+4x3×1
Multiply the terms
More Steps

Evaluate
4x3×2x
Multiply the numbers
8x3×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
8x4
x7−2x6+x5−4x6−(−8x5)−4x4+4x5−8x4+4x3×1
Any expression multiplied by 1 remains the same
x7−2x6+x5−4x6−(−8x5)−4x4+4x5−8x4+4x3
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x7−2x6+x5−4x6+8x5−4x4+4x5−8x4+4x3
Subtract the terms
More Steps

Evaluate
−2x6−4x6
Collect like terms by calculating the sum or difference of their coefficients
(−2−4)x6
Subtract the numbers
−6x6
x7−6x6+x5+8x5−4x4+4x5−8x4+4x3
Add the terms
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Evaluate
x5+8x5+4x5
Collect like terms by calculating the sum or difference of their coefficients
(1+8+4)x5
Add the numbers
13x5
x7−6x6+13x5−4x4−8x4+4x3
Solution
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Evaluate
−4x4−8x4
Collect like terms by calculating the sum or difference of their coefficients
(−4−8)x4
Subtract the numbers
−12x4
x7−6x6+13x5−12x4+4x3
Show Solution

Find the roots
x1=0,x2=1,x3=2
Evaluate
(x−2)(x−1)2(x×1)3(x−2)
To find the roots of the expression,set the expression equal to 0
(x−2)(x−1)2(x×1)3(x−2)=0
Any expression multiplied by 1 remains the same
(x−2)(x−1)2x3(x−2)=0
Multiply the terms
More Steps

Multiply the terms
(x−2)(x−1)2x3(x−2)
Use the commutative property to reorder the terms
(x−2)x3(x−1)2(x−2)
Multiply the terms
(x−2)2x3(x−1)2
(x−2)2x3(x−1)2=0
Separate the equation into 3 possible cases
(x−2)2=0x3=0(x−1)2=0
Solve the equation
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Evaluate
(x−2)2=0
The only way a power can be 0 is when the base equals 0
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x3=0(x−1)2=0
The only way a power can be 0 is when the base equals 0
x=2x=0(x−1)2=0
Solve the equation
More Steps

Evaluate
(x−1)2=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=2x=0x=1
Solution
x1=0,x2=1,x3=2
Show Solution
