Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x8−32x6+256x4
Evaluate
(x4−4x2×4)2
Multiply the terms
(x4−16x2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(x4)2−2x4×16x2+(16x2)2
Solution
x8−32x6+256x4
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Factor the expression
x4(x−4)2(x+4)2
Evaluate
(x4−4x2×4)2
Multiply the terms
(x4−16x2)2
Factor the expression
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Evaluate
x4−16x2
Rewrite the expression
x2×x2−x2×16
Factor out x2 from the expression
x2(x2−16)
Use a2−b2=(a−b)(a+b) to factor the expression
x2(x−4)(x+4)
(x2(x−4)(x+4))2
Solution
x4(x−4)2(x+4)2
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Find the roots
x1=−4,x2=0,x3=4
Evaluate
(x4−4x2×4)2
To find the roots of the expression,set the expression equal to 0
(x4−4x2×4)2=0
Multiply the terms
(x4−16x2)2=0
The only way a power can be 0 is when the base equals 0
x4−16x2=0
Factor the expression
x2(x2−16)=0
Separate the equation into 2 possible cases
x2=0x2−16=0
The only way a power can be 0 is when the base equals 0
x=0x2−16=0
Solve the equation
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Evaluate
x2−16=0
Move the constant to the right-hand side and change its sign
x2=0+16
Removing 0 doesn't change the value,so remove it from the expression
x2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±16
Simplify the expression
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Evaluate
16
Write the number in exponential form with the base of 4
42
Reduce the index of the radical and exponent with 2
4
x=±4
Separate the equation into 2 possible cases
x=4x=−4
x=0x=4x=−4
Solution
x1=−4,x2=0,x3=4
Show Solution