Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
a6(1−a)(1+a)
Evaluate
a6−a8
Factor out a6 from the expression
a6(1−a2)
Solution
More Steps
Evaluate
1−a2
Rewrite the expression in exponential form
12−a2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−a)(1+a)
a6(1−a)(1+a)
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Find the roots
a1=−1,a2=0,a3=1
Evaluate
a6−a8
To find the roots of the expression,set the expression equal to 0
a6−a8=0
Factor the expression
a6(1−a2)=0
Separate the equation into 2 possible cases
a6=01−a2=0
The only way a power can be 0 is when the base equals 0
a=01−a2=0
Solve the equation
More Steps
Evaluate
1−a2=0
Move the constant to the right-hand side and change its sign
−a2=0−1
Removing 0 doesn't change the value,so remove it from the expression
−a2=−1
Change the signs on both sides of the equation
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
a=0a=1a=−1
Solution
a1=−1,a2=0,a3=1
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