Question
Simplify the expression
1−5x+8x2−4x3
Evaluate
(1−2x)2(1−x)
Expand the expression
More Steps

Evaluate
(1−2x)2
Use (a−b)2=a2−2ab+b2 to expand the expression
12−2×1×2x+(2x)2
Calculate
1−4x+4x2
(1−4x+4x2)(1−x)
Apply the distributive property
1×1−1×x−4x×1−(−4x×x)+4x2×1−4x2×x
Any expression multiplied by 1 remains the same
1−1×x−4x×1−(−4x×x)+4x2×1−4x2×x
Any expression multiplied by 1 remains the same
1−x−4x×1−(−4x×x)+4x2×1−4x2×x
Any expression multiplied by 1 remains the same
1−x−4x−(−4x×x)+4x2×1−4x2×x
Multiply the terms
1−x−4x−(−4x2)+4x2×1−4x2×x
Any expression multiplied by 1 remains the same
1−x−4x−(−4x2)+4x2−4x2×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
1−x−4x−(−4x2)+4x2−4x3
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1−x−4x+4x2+4x2−4x3
Subtract the terms
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Evaluate
−x−4x
Collect like terms by calculating the sum or difference of their coefficients
(−1−4)x
Subtract the numbers
−5x
1−5x+4x2+4x2−4x3
Solution
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Evaluate
4x2+4x2
Collect like terms by calculating the sum or difference of their coefficients
(4+4)x2
Add the numbers
8x2
1−5x+8x2−4x3
Show Solution

Find the roots
x1=21,x2=1
Alternative Form
x1=0.5,x2=1
Evaluate
(1−2x)2(1−x)
To find the roots of the expression,set the expression equal to 0
(1−2x)2(1−x)=0
Separate the equation into 2 possible cases
(1−2x)2=01−x=0
Solve the equation
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Evaluate
(1−2x)2=0
The only way a power can be 0 is when the base equals 0
1−2x=0
Move the constant to the right-hand side and change its sign
−2x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−2x=−1
Change the signs on both sides of the equation
2x=1
Divide both sides
22x=21
Divide the numbers
x=21
x=211−x=0
Solve the equation
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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=21x=1
Solution
x1=21,x2=1
Alternative Form
x1=0.5,x2=1
Show Solution
