Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
a4a8−4a6+6a4−4a2+1
Evaluate
(a−a1)4
Subtract the terms
More Steps
Simplify
a−a1
Reduce fractions to a common denominator
aa×a−a1
Write all numerators above the common denominator
aa×a−1
Multiply the terms
aa2−1
(aa2−1)4
Rewrite the expression
a4(a2−1)4
Solution
a4a8−4a6+6a4−4a2+1
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Find the excluded values
a=0
Evaluate
(a−a1)4
Solution
a=0
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Find the roots
a1=−1,a2=1
Evaluate
(a−a1)4
To find the roots of the expression,set the expression equal to 0
(a−a1)4=0
Find the domain
(a−a1)4=0,a=0
Calculate
(a−a1)4=0
Subtract the terms
More Steps
Simplify
a−a1
Reduce fractions to a common denominator
aa×a−a1
Write all numerators above the common denominator
aa×a−1
Multiply the terms
aa2−1
(aa2−1)4=0
The only way a power can be 0 is when the base equals 0
aa2−1=0
Cross multiply
a2−1=a×0
Simplify the equation
a2−1=0
Move the constant to the right side
a2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±1
Simplify the expression
a=±1
Separate the equation into 2 possible cases
a=1a=−1
Check if the solution is in the defined range
a=1a=−1,a=0
Find the intersection of the solution and the defined range
a=1a=−1
Solution
a1=−1,a2=1
Show Solution