Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−a2−4a+4
Evaluate
(a−2)2−2a2
Expand the expression
a2−4a+4−2a2
Solution
More Steps
Evaluate
a2−2a2
Collect like terms by calculating the sum or difference of their coefficients
(1−2)a2
Subtract the numbers
−a2
−a2−4a+4
Show Solution
Find the roots
a1=−2−22,a2=−2+22
Alternative Form
a1≈−4.828427,a2≈0.828427
Evaluate
(a−2)2−2(a2)
To find the roots of the expression,set the expression equal to 0
(a−2)2−2(a2)=0
Calculate
(a−2)2−2a2=0
Calculate
More Steps
Evaluate
(a−2)2−2a2
Expand the expression
a2−4a+4−2a2
Subtract the terms
More Steps
Evaluate
a2−2a2
Collect like terms by calculating the sum or difference of their coefficients
(1−2)a2
Subtract the numbers
−a2
−a2−4a+4
−a2−4a+4=0
Multiply both sides
a2+4a−4=0
Substitute a=1,b=4 and c=−4 into the quadratic formula a=2a−b±b2−4ac
a=2−4±42−4(−4)
Simplify the expression
More Steps
Evaluate
42−4(−4)
Multiply the numbers
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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
a=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
a=2−4±42
Separate the equation into 2 possible cases
a=2−4+42a=2−4−42
Simplify the expression
More Steps
Evaluate
a=2−4+42
Divide the terms
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Evaluate
2−4+42
Rewrite the expression
22(−2+22)
Reduce the fraction
−2+22
a=−2+22
a=−2+22a=2−4−42
Simplify the expression
More Steps
Evaluate
a=2−4−42
Divide the terms
More Steps
Evaluate
2−4−42
Rewrite the expression
22(−2−22)
Reduce the fraction
−2−22
a=−2−22
a=−2+22a=−2−22
Solution
a1=−2−22,a2=−2+22
Alternative Form
a1≈−4.828427,a2≈0.828427
Show Solution