Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x4−324x2
Evaluate
x4−12x2×27
Solution
x4−324x2
Show Solution
Factor the expression
x2(x−18)(x+18)
Evaluate
x4−12x2×27
Evaluate
x4−324x2
Factor out x2 from the expression
x2(x2−324)
Solution
More Steps
Evaluate
x2−324
Rewrite the expression in exponential form
x2−182
Use a2−b2=(a−b)(a+b) to factor the expression
(x−18)(x+18)
x2(x−18)(x+18)
Show Solution
Find the roots
x1=−18,x2=0,x3=18
Evaluate
x4−12x2×27
To find the roots of the expression,set the expression equal to 0
x4−12x2×27=0
Multiply the terms
x4−324x2=0
Factor the expression
x2(x2−324)=0
Separate the equation into 2 possible cases
x2=0x2−324=0
The only way a power can be 0 is when the base equals 0
x=0x2−324=0
Solve the equation
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Evaluate
x2−324=0
Move the constant to the right-hand side and change its sign
x2=0+324
Removing 0 doesn't change the value,so remove it from the expression
x2=324
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±324
Simplify the expression
More Steps
Evaluate
324
Write the number in exponential form with the base of 18
182
Reduce the index of the radical and exponent with 2
18
x=±18
Separate the equation into 2 possible cases
x=18x=−18
x=0x=18x=−18
Solution
x1=−18,x2=0,x3=18
Show Solution