Question
Simplify the expression
x2−64x6
Evaluate
x2−16x6×4
Solution
x2−64x6
Show Solution

Factor the expression
x2(1−8x2)(1+8x2)
Evaluate
x2−16x6×4
Evaluate
x2−64x6
Factor out x2 from the expression
x2(1−64x4)
Solution
More Steps

Evaluate
1−64x4
Rewrite the expression in exponential form
12−(8x2)2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−8x2)(1+8x2)
x2(1−8x2)(1+8x2)
Show Solution

Find the roots
x1=−42,x2=0,x3=42
Alternative Form
x1≈−0.353553,x2=0,x3≈0.353553
Evaluate
x2−16x6×4
To find the roots of the expression,set the expression equal to 0
x2−16x6×4=0
Multiply the terms
x2−64x6=0
Factor the expression
x2(1−64x4)=0
Separate the equation into 2 possible cases
x2=01−64x4=0
The only way a power can be 0 is when the base equals 0
x=01−64x4=0
Solve the equation
More Steps

Evaluate
1−64x4=0
Move the constant to the right-hand side and change its sign
−64x4=0−1
Removing 0 doesn't change the value,so remove it from the expression
−64x4=−1
Change the signs on both sides of the equation
64x4=1
Divide both sides
6464x4=641
Divide the numbers
x4=641
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4641
Simplify the expression
More Steps

Evaluate
4641
To take a root of a fraction,take the root of the numerator and denominator separately
46441
Simplify the radical expression
4641
Simplify the radical expression
221
Multiply by the Conjugate
22×22
Multiply the numbers
42
x=±42
Separate the equation into 2 possible cases
x=42x=−42
x=0x=42x=−42
Solution
x1=−42,x2=0,x3=42
Alternative Form
x1≈−0.353553,x2=0,x3≈0.353553
Show Solution
