Question
Simplify the expression
y2−4+4y
Evaluate
2y2−(2−y)2
Expand the expression
2y2−4+4y−y2
Solution
More Steps

Evaluate
2y2−y2
Collect like terms by calculating the sum or difference of their coefficients
(2−1)y2
Subtract the numbers
y2
y2−4+4y
Show Solution

Find the roots
y1=−2−22,y2=−2+22
Alternative Form
y1≈−4.828427,y2≈0.828427
Evaluate
2y2−(2−y)2
To find the roots of the expression,set the expression equal to 0
2y2−(2−y)2=0
Calculate
More Steps

Evaluate
2y2−(2−y)2
Expand the expression
2y2−4+4y−y2
Subtract the terms
More Steps

Evaluate
2y2−y2
Collect like terms by calculating the sum or difference of their coefficients
(2−1)y2
Subtract the numbers
y2
y2−4+4y
y2−4+4y=0
Rewrite in standard form
y2+4y−4=0
Substitute a=1,b=4 and c=−4 into the quadratic formula y=2a−b±b2−4ac
y=2−4±42−4(−4)
Simplify the expression
More Steps

Evaluate
42−4(−4)
Multiply the numbers
More Steps

Evaluate
4(−4)
Multiplying or dividing an odd number of negative terms equals a negative
−4×4
Multiply the numbers
−16
42−(−16)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+16
Evaluate the power
16+16
Add the numbers
32
y=2−4±32
Simplify the radical expression
More Steps

Evaluate
32
Write the expression as a product where the root of one of the factors can be evaluated
16×2
Write the number in exponential form with the base of 4
42×2
The root of a product is equal to the product of the roots of each factor
42×2
Reduce the index of the radical and exponent with 2
42
y=2−4±42
Separate the equation into 2 possible cases
y=2−4+42y=2−4−42
Simplify the expression
More Steps

Evaluate
y=2−4+42
Divide the terms
More Steps

Evaluate
2−4+42
Rewrite the expression
22(−2+22)
Reduce the fraction
−2+22
y=−2+22
y=−2+22y=2−4−42
Simplify the expression
More Steps

Evaluate
y=2−4−42
Divide the terms
More Steps

Evaluate
2−4−42
Rewrite the expression
22(−2−22)
Reduce the fraction
−2−22
y=−2−22
y=−2+22y=−2−22
Solution
y1=−2−22,y2=−2+22
Alternative Form
y1≈−4.828427,y2≈0.828427
Show Solution
