Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x2−x6
Evaluate
(−x)2−x6
Solution
x2−x6
Show Solution
Factor the expression
x2(1−x)(1+x)(1+x2)
Evaluate
((−x)2)−x6
Evaluate
More Steps
Evaluate
((−x)2)
Evaluate
(−x)2
Determine the sign
x2
x2−x6
Factor out x2 from the expression
x2(1−x4)
Factor the expression
More Steps
Evaluate
1−x4
Rewrite the expression in exponential form
12−(x2)2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x2)(1+x2)
x2(1−x2)(1+x2)
Solution
More Steps
Evaluate
1−x2
Rewrite the expression in exponential form
12−x2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x)(1+x)
x2(1−x)(1+x)(1+x2)
Show Solution
Find the roots
x1=−1,x2=0,x3=1
Evaluate
((−x)2)−x6
To find the roots of the expression,set the expression equal to 0
((−x)2)−x6=0
Calculate
(−x)2−x6=0
Rewrite the expression
x2−x6=0
Factor the expression
x2(1−x4)=0
Separate the equation into 2 possible cases
x2=01−x4=0
The only way a power can be 0 is when the base equals 0
x=01−x4=0
Solve the equation
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Evaluate
1−x4=0
Move the constant to the right-hand side and change its sign
−x4=0−1
Removing 0 doesn't change the value,so remove it from the expression
−x4=−1
Change the signs on both sides of the equation
x4=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±41
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
x=0x=1x=−1
Solution
x1=−1,x2=0,x3=1
Show Solution