Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
31a2(a−1)(a+1)
Evaluate
31a4−31a2
Factor out 31a2 from the expression
31a2(a2−1)
Solution
More Steps
Evaluate
a2−1
Rewrite the expression in exponential form
a2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(a−1)(a+1)
31a2(a−1)(a+1)
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Find the roots
a1=−1,a2=0,a3=1
Evaluate
31a4−31a2
To find the roots of the expression,set the expression equal to 0
31a4−31a2=0
Factor the expression
31a2(a2−1)=0
Divide both sides
a2(a2−1)=0
Separate the equation into 2 possible cases
a2=0a2−1=0
The only way a power can be 0 is when the base equals 0
a=0a2−1=0
Solve the equation
More Steps
Evaluate
a2−1=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
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
Show Solution