Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
5y2(1−y2−2y)
Evaluate
5y2−5y4−10y3
Rewrite the expression
5y2−5y2×y2−5y2×2y
Solution
5y2(1−y2−2y)
Show Solution
Find the roots
y1=−1−2,y2=0,y3=−1+2
Alternative Form
y1≈−2.414214,y2=0,y3≈0.414214
Evaluate
5y2−5y4−10y3
To find the roots of the expression,set the expression equal to 0
5y2−5y4−10y3=0
Factor the expression
5y2(1−y2−2y)=0
Divide both sides
y2(1−y2−2y)=0
Separate the equation into 2 possible cases
y2=01−y2−2y=0
The only way a power can be 0 is when the base equals 0
y=01−y2−2y=0
Solve the equation
More Steps
Evaluate
1−y2−2y=0
Rewrite in standard form
−y2−2y+1=0
Multiply both sides
y2+2y−1=0
Substitute a=1,b=2 and c=−1 into the quadratic formula y=2a−b±b2−4ac
y=2−2±22−4(−1)
Simplify the expression
More Steps
Evaluate
22−4(−1)
Simplify
22−(−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22+4
Evaluate the power
4+4
Add the numbers
8
y=2−2±8
Simplify the radical expression
More Steps
Evaluate
8
Write the expression as a product where the root of one of the factors can be evaluated
4×2
Write the number in exponential form with the base of 2
22×2
The root of a product is equal to the product of the roots of each factor
22×2
Reduce the index of the radical and exponent with 2
22
y=2−2±22
Separate the equation into 2 possible cases
y=2−2+22y=2−2−22
Simplify the expression
y=−1+2y=2−2−22
Simplify the expression
y=−1+2y=−1−2
y=0y=−1+2y=−1−2
Solution
y1=−1−2,y2=0,y3=−1+2
Alternative Form
y1≈−2.414214,y2=0,y3≈0.414214
Show Solution