Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
2y6−2y
Evaluate
y6×2−2y
Solution
2y6−2y
Show Solution
Factor the expression
2y(y−1)(y4+y3+y2+y+1)
Evaluate
y6×2−2y
Use the commutative property to reorder the terms
2y6−2y
Rewrite the expression
2y×y5−2y
Factor out 2y from the expression
2y(y5−1)
Solution
More Steps
Evaluate
y5−1
Calculate
y5+y4+y3+y2+y−y4−y3−y2−y−1
Rewrite the expression
y×y4+y×y3+y×y2+y×y+y−y4−y3−y2−y−1
Factor out y from the expression
y(y4+y3+y2+y+1)−y4−y3−y2−y−1
Factor out −1 from the expression
y(y4+y3+y2+y+1)−(y4+y3+y2+y+1)
Factor out y4+y3+y2+y+1 from the expression
(y−1)(y4+y3+y2+y+1)
2y(y−1)(y4+y3+y2+y+1)
Show Solution
Find the roots
y1=0,y2=1
Evaluate
y6×2−2y
To find the roots of the expression,set the expression equal to 0
y6×2−2y=0
Use the commutative property to reorder the terms
2y6−2y=0
Factor the expression
2y(y5−1)=0
Divide both sides
y(y5−1)=0
Separate the equation into 2 possible cases
y=0y5−1=0
Solve the equation
More Steps
Evaluate
y5−1=0
Move the constant to the right-hand side and change its sign
y5=0+1
Removing 0 doesn't change the value,so remove it from the expression
y5=1
Take the 5-th root on both sides of the equation
5y5=51
Calculate
y=51
Simplify the root
y=1
y=0y=1
Solution
y1=0,y2=1
Show Solution