Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
25x4−10x6+x8
Evaluate
(5x2−x4)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(5x2)2−2×5x2×x4+(x4)2
Solution
25x4−10x6+x8
Show Solution
Factor the expression
x4(5−x2)2
Evaluate
(5x2−x4)2
Factor the expression
More Steps
Evaluate
5x2−x4
Rewrite the expression
x2×5−x2×x2
Factor out x2 from the expression
x2(5−x2)
(x2(5−x2))2
Solution
x4(5−x2)2
Show Solution
Find the roots
x1=−5,x2=0,x3=5
Alternative Form
x1≈−2.236068,x2=0,x3≈2.236068
Evaluate
(5x2−x4)2
To find the roots of the expression,set the expression equal to 0
(5x2−x4)2=0
The only way a power can be 0 is when the base equals 0
5x2−x4=0
Factor the expression
x2(5−x2)=0
Separate the equation into 2 possible cases
x2=05−x2=0
The only way a power can be 0 is when the base equals 0
x=05−x2=0
Solve the equation
More Steps
Evaluate
5−x2=0
Move the constant to the right-hand side and change its sign
−x2=0−5
Removing 0 doesn't change the value,so remove it from the expression
−x2=−5
Change the signs on both sides of the equation
x2=5
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±5
Separate the equation into 2 possible cases
x=5x=−5
x=0x=5x=−5
Solution
x1=−5,x2=0,x3=5
Alternative Form
x1≈−2.236068,x2=0,x3≈2.236068
Show Solution