Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x4−1024x2
Evaluate
x4−16x2×64
Solution
x4−1024x2
Show Solution
Factor the expression
x2(x−32)(x+32)
Evaluate
x4−16x2×64
Evaluate
x4−1024x2
Factor out x2 from the expression
x2(x2−1024)
Solution
More Steps
Evaluate
x2−1024
Rewrite the expression in exponential form
x2−322
Use a2−b2=(a−b)(a+b) to factor the expression
(x−32)(x+32)
x2(x−32)(x+32)
Show Solution
Find the roots
x1=−32,x2=0,x3=32
Evaluate
x4−16x2×64
To find the roots of the expression,set the expression equal to 0
x4−16x2×64=0
Multiply the terms
x4−1024x2=0
Factor the expression
x2(x2−1024)=0
Separate the equation into 2 possible cases
x2=0x2−1024=0
The only way a power can be 0 is when the base equals 0
x=0x2−1024=0
Solve the equation
More Steps
Evaluate
x2−1024=0
Move the constant to the right-hand side and change its sign
x2=0+1024
Removing 0 doesn't change the value,so remove it from the expression
x2=1024
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±1024
Simplify the expression
More Steps
Evaluate
1024
Write the number in exponential form with the base of 32
322
Reduce the index of the radical and exponent with 2
32
x=±32
Separate the equation into 2 possible cases
x=32x=−32
x=0x=32x=−32
Solution
x1=−32,x2=0,x3=32
Show Solution