Question
Simplify the expression
1−4x2+4x41
Evaluate
(1−2x2)−2
Express with a positive exponent using a−n=an1
(1−2x2)21
Solution
More Steps

Evaluate
(1−2x2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
12−2×1×2x2+(2x2)2
Calculate
1−4x2+4x4
1−4x2+4x41
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Find the roots
x∈∅
Evaluate
(1−2x2)−2
To find the roots of the expression,set the expression equal to 0
(1−2x2)−2=0
Find the domain
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Evaluate
1−2x2=0
Rewrite the expression
−2x2=−1
Change the signs on both sides of the equation
2x2=1
Divide both sides
22x2=21
Divide the numbers
x2=21
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±21
Simplify the expression
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Evaluate
21
To take a root of a fraction,take the root of the numerator and denominator separately
21
Simplify the radical expression
21
Multiply by the Conjugate
2×22
When a square root of an expression is multiplied by itself,the result is that expression
22
x=±22
Separate the inequality into 2 possible cases
{x=22x=−22
Find the intersection
x∈(−∞,−22)∪(−22,22)∪(22,+∞)
(1−2x2)−2=0,x∈(−∞,−22)∪(−22,22)∪(22,+∞)
Calculate
(1−2x2)−2=0
Rewrite the expression
(1−2x2)21=0
Cross multiply
1=(1−2x2)2×0
Simplify the equation
1=0
Solution
x∈∅
Show Solution
