Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
y3(1−y)(1+y)
Evaluate
y3−y5
Factor out y3 from the expression
y3(1−y2)
Solution
More Steps
Evaluate
1−y2
Rewrite the expression in exponential form
12−y2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−y)(1+y)
y3(1−y)(1+y)
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Find the roots
y1=−1,y2=0,y3=1
Evaluate
y3−y5
To find the roots of the expression,set the expression equal to 0
y3−y5=0
Factor the expression
y3(1−y2)=0
Separate the equation into 2 possible cases
y3=01−y2=0
The only way a power can be 0 is when the base equals 0
y=01−y2=0
Solve the equation
More Steps
Evaluate
1−y2=0
Move the constant to the right-hand side and change its sign
−y2=0−1
Removing 0 doesn't change the value,so remove it from the expression
−y2=−1
Change the signs on both sides of the equation
y2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±1
Simplify the expression
y=±1
Separate the equation into 2 possible cases
y=1y=−1
y=0y=1y=−1
Solution
y1=−1,y2=0,y3=1
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