Question
Simplify the expression
−x4−8x10
Evaluate
−x4−x3×2x2×4x5
Solution
More Steps

Evaluate
−x3×2x2×4x5
Multiply the terms with the same base by adding their exponents
−x3+2+5×2×4
Add the numbers
−x10×2×4
Multiply the terms
−x10×8
Use the commutative property to reorder the terms
−8x10
−x4−8x10
Show Solution

Factor the expression
−x4(1+2x2)(1−2x2+4x4)
Evaluate
−x4−x3×2x2×4x5
Evaluate
More Steps

Evaluate
x3×2x2×4x5
Multiply the terms with the same base by adding their exponents
x3+2+5×2×4
Add the numbers
x10×2×4
Multiply the terms
x10×8
Use the commutative property to reorder the terms
8x10
−x4−8x10
Factor out −x4 from the expression
−x4(1+8x6)
Solution
More Steps

Evaluate
1+8x6
Rewrite the expression in exponential form
13+(2x2)3
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(1+2x2)(12−1×2x2+(2x2)2)
1 raised to any power equals to 1
(1+2x2)(1−1×2x2+(2x2)2)
Any expression multiplied by 1 remains the same
(1+2x2)(1−2x2+(2x2)2)
Evaluate
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Evaluate
(2x2)2
To raise a product to a power,raise each factor to that power
22(x2)2
Evaluate the power
4(x2)2
Evaluate the power
4x4
(1+2x2)(1−2x2+4x4)
−x4(1+2x2)(1−2x2+4x4)
Show Solution

Find the roots
x1=−46+42i,x2=46−42i,x3=0
Alternative Form
x1≈−0.612372+0.353553i,x2≈0.612372−0.353553i,x3=0
Evaluate
−x4−x3×2x2×4x5
To find the roots of the expression,set the expression equal to 0
−x4−x3×2x2×4x5=0
Multiply
More Steps

Multiply the terms
x3×2x2×4x5
Multiply the terms with the same base by adding their exponents
x3+2+5×2×4
Add the numbers
x10×2×4
Multiply the terms
x10×8
Use the commutative property to reorder the terms
8x10
−x4−8x10=0
Factor the expression
−x4(1+8x6)=0
Divide both sides
x4(1+8x6)=0
Separate the equation into 2 possible cases
x4=01+8x6=0
The only way a power can be 0 is when the base equals 0
x=01+8x6=0
Solve the equation
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Evaluate
1+8x6=0
Move the constant to the right-hand side and change its sign
8x6=0−1
Removing 0 doesn't change the value,so remove it from the expression
8x6=−1
Divide both sides
88x6=8−1
Divide the numbers
x6=8−1
Use b−a=−ba=−ba to rewrite the fraction
x6=−81
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±6−81
Simplify the expression
More Steps

Evaluate
6−81
To take a root of a fraction,take the root of the numerator and denominator separately
6−861
Simplify the radical expression
6−81
Simplify the radical expression
26+22i1
Multiply by the Conjugate
(26+22i)(26−22i)26−22i
Calculate
226−22i
Simplify
46−42i
x=±(46−42i)
Separate the equation into 2 possible cases
x=46−42ix=−46+42i
x=0x=46−42ix=−46+42i
Solution
x1=−46+42i,x2=46−42i,x3=0
Alternative Form
x1≈−0.612372+0.353553i,x2≈0.612372−0.353553i,x3=0
Show Solution
