Question
Simplify the expression
y3−2y2+y
Evaluate
(y−1)(y×1)(y−1)
Remove the parentheses
(y−1)y×1×(y−1)
Any expression multiplied by 1 remains the same
(y−1)y(y−1)
Multiply the first two terms
y(y−1)(y−1)
Multiply the terms
y(y−1)2
Expand the expression
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Evaluate
(y−1)2
Use (a−b)2=a2−2ab+b2 to expand the expression
y2−2y×1+12
Calculate
y2−2y+1
y(y2−2y+1)
Apply the distributive property
y×y2−y×2y+y×1
Multiply the terms
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Evaluate
y×y2
Use the product rule an×am=an+m to simplify the expression
y1+2
Add the numbers
y3
y3−y×2y+y×1
Multiply the terms
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Evaluate
y×2y
Use the commutative property to reorder the terms
2y×y
Multiply the terms
2y2
y3−2y2+y×1
Solution
y3−2y2+y
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Find the roots
y1=0,y2=1
Evaluate
(y−1)(y×1)(y−1)
To find the roots of the expression,set the expression equal to 0
(y−1)(y×1)(y−1)=0
Any expression multiplied by 1 remains the same
(y−1)y(y−1)=0
Multiply the terms
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Multiply the terms
(y−1)y(y−1)
Multiply the first two terms
y(y−1)(y−1)
Multiply the terms
y(y−1)2
y(y−1)2=0
Separate the equation into 2 possible cases
y=0(y−1)2=0
Solve the equation
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Evaluate
(y−1)2=0
The only way a power can be 0 is when the base equals 0
y−1=0
Move the constant to the right-hand side and change its sign
y=0+1
Removing 0 doesn't change the value,so remove it from the expression
y=1
y=0y=1
Solution
y1=0,y2=1
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