Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
16x216−8x2+x4
Evaluate
(8x8−2x)2
Subtract the terms
More Steps
Simplify
x8−2x
Reduce fractions to a common denominator
x8−x2x×x
Write all numerators above the common denominator
x8−2x×x
Multiply the terms
x8−2x2
8x8−2x22
Divide the terms
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Evaluate
8x8−2x2
Multiply by the reciprocal
x8−2x2×81
Rewrite the expression
x2(4−x2)×81
Cancel out the common factor 2
x4−x2×41
Multiply the terms
x×44−x2
Use the commutative property to reorder the terms
4x4−x2
(4x4−x2)2
Rewrite the expression
(4x)2(4−x2)2
Evaluate the power
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Evaluate the power
(4x)2
To raise a product to a power,raise each factor to that power
42x2
Evaluate the power
16x2
16x2(4−x2)2
Solution
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Evaluate
(4−x2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
42−2×4x2+(x2)2
Calculate
16−8x2+x4
16x216−8x2+x4
Show Solution
Find the excluded values
x=0
Evaluate
(8(x8)−2x)2
Solution
x=0
Show Solution
Find the roots
x1=−2,x2=2
Evaluate
(8(x8)−2x)2
To find the roots of the expression,set the expression equal to 0
(8(x8)−2x)2=0
Find the domain
(8(x8)−2x)2=0,x=0
Calculate
(8(x8)−2x)2=0
Remove the unnecessary parentheses
(8x8−2x)2=0
Subtract the terms
More Steps
Simplify
x8−2x
Reduce fractions to a common denominator
x8−x2x×x
Write all numerators above the common denominator
x8−2x×x
Multiply the terms
x8−2x2
8x8−2x22=0
Divide the terms
More Steps
Evaluate
8x8−2x2
Multiply by the reciprocal
x8−2x2×81
Rewrite the expression
x2(4−x2)×81
Cancel out the common factor 2
x4−x2×41
Multiply the terms
x×44−x2
Use the commutative property to reorder the terms
4x4−x2
(4x4−x2)2=0
The only way a power can be 0 is when the base equals 0
4x4−x2=0
Cross multiply
4−x2=4x×0
Simplify the equation
4−x2=0
Rewrite the expression
−x2=−4
Change the signs on both sides of the equation
x2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4
Simplify the expression
More Steps
Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
x=±2
Separate the equation into 2 possible cases
x=2x=−2
Check if the solution is in the defined range
x=2x=−2,x=0
Find the intersection of the solution and the defined range
x=2x=−2
Solution
x1=−2,x2=2
Show Solution