Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
g6−g2
Evaluate
g6×1−g2
Solution
g6−g2
Show Solution
Factor the expression
g2(g−1)(g+1)(g2+1)
Evaluate
g6×1−g2
Any expression multiplied by 1 remains the same
g6−g2
Factor out g2 from the expression
g2(g4−1)
Factor the expression
More Steps
Evaluate
g4−1
Rewrite the expression in exponential form
(g2)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(g2−1)(g2+1)
g2(g2−1)(g2+1)
Solution
More Steps
Evaluate
g2−1
Rewrite the expression in exponential form
g2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(g−1)(g+1)
g2(g−1)(g+1)(g2+1)
Show Solution
Find the roots
g1=−1,g2=0,g3=1
Evaluate
g6×1−g2
To find the roots of the expression,set the expression equal to 0
g6×1−g2=0
Any expression multiplied by 1 remains the same
g6−g2=0
Factor the expression
g2(g4−1)=0
Separate the equation into 2 possible cases
g2=0g4−1=0
The only way a power can be 0 is when the base equals 0
g=0g4−1=0
Solve the equation
More Steps
Evaluate
g4−1=0
Move the constant to the right-hand side and change its sign
g4=0+1
Removing 0 doesn't change the value,so remove it from the expression
g4=1
Take the root of both sides of the equation and remember to use both positive and negative roots
g=±41
Simplify the expression
g=±1
Separate the equation into 2 possible cases
g=1g=−1
g=0g=1g=−1
Solution
g1=−1,g2=0,g3=1
Show Solution