Question
Simplify the expression
6x8−12x12
Evaluate
(x−121x3×24x2)((3×12x2)x3×24x2)
Remove the parentheses
(x−121x3×24x2)×3×12x2x3×24x2
Multiply
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Multiply the terms
121x3×24x2
Multiply the terms
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Evaluate
121×24
Reduce the numbers
1×2
Simplify
2
2x3×x2
Multiply the terms with the same base by adding their exponents
2x3+2
Add the numbers
2x5
(x−2x5)×3×12x2x3×24x2
Multiply the terms
(x−2x5)×72×12x2x3×x2
Multiply the terms with the same base by adding their exponents
(x−2x5)×72×12x2x3+2
Add the numbers
(x−2x5)×72×12x2x5
Multiply the terms
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Evaluate
72×12x2x5
Cancel out the common factor 12
6x2×x5
Multiply the terms
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Evaluate
x2×x5
Use the product rule an×am=an+m to simplify the expression
x2+5
Add the numbers
x7
6x7
(x−2x5)×6x7
Multiply the terms
6x7(x−2x5)
Apply the distributive property
6x7×x−6x7×2x5
Multiply the terms
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Evaluate
x7×x
Use the product rule an×am=an+m to simplify the expression
x7+1
Add the numbers
x8
6x8−6x7×2x5
Solution
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Evaluate
6x7×2x5
Multiply the numbers
12x7×x5
Multiply the terms
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Evaluate
x7×x5
Use the product rule an×am=an+m to simplify the expression
x7+5
Add the numbers
x12
12x12
6x8−12x12
Show Solution

Factor the expression
6x8(1−2x4)
Evaluate
(x−121x3×24x2)((3×12x2)x3×24x2)
Remove the parentheses
(x−121x3×24x2)×3×12x2x3×24x2
Multiply
More Steps

Multiply the terms
121x3×24x2
Multiply the terms
More Steps

Evaluate
121×24
Reduce the numbers
1×2
Simplify
2
2x3×x2
Multiply the terms with the same base by adding their exponents
2x3+2
Add the numbers
2x5
(x−2x5)×3×12x2x3×24x2
Multiply the terms
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Multiply the terms
3×12x2
Cancel out the common factor 3
1×4x2
Multiply the terms
4x2
(x−2x5)×4x2x3×24x2
Multiply
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Multiply the terms
4x2x3×24x2
Multiply the terms with the same base by adding their exponents
4x2x3+2×24
Add the numbers
4x2x5×24
Multiply the terms
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Multiply the terms
4x2x5
Multiply the terms
4x2×x5
Multiply the terms
4x7
4x7×24
Cancel out the common factor 4
x7×6
Use the commutative property to reorder the terms
6x7
(x−2x5)×6x7
Multiply the terms
6x7(x−2x5)
Factor the expression
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Evaluate
x−2x5
Rewrite the expression
x−x×2x4
Factor out x from the expression
x(1−2x4)
6x7×x(1−2x4)
Solution
6x8(1−2x4)
Show Solution

Find the roots
x1=−248,x2=0,x3=248
Alternative Form
x1≈−0.840896,x2=0,x3≈0.840896
Evaluate
(x−121x3×24x2)((3×12x2)x3×24x2)
To find the roots of the expression,set the expression equal to 0
(x−121x3×24x2)((3×12x2)x3×24x2)=0
Multiply
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Multiply the terms
121x3×24x2
Multiply the terms
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Evaluate
121×24
Reduce the numbers
1×2
Simplify
2
2x3×x2
Multiply the terms with the same base by adding their exponents
2x3+2
Add the numbers
2x5
(x−2x5)((3×12x2)x3×24x2)=0
Multiply the terms
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Multiply the terms
3×12x2
Cancel out the common factor 3
1×4x2
Multiply the terms
4x2
(x−2x5)(4x2x3×24x2)=0
Multiply
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Multiply the terms
4x2x3×24x2
Multiply the terms with the same base by adding their exponents
4x2x3+2×24
Add the numbers
4x2x5×24
Multiply the terms
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Multiply the terms
4x2x5
Multiply the terms
4x2×x5
Multiply the terms
4x7
4x7×24
Cancel out the common factor 4
x7×6
Use the commutative property to reorder the terms
6x7
(x−2x5)×6x7=0
Multiply the terms
6x7(x−2x5)=0
Elimination the left coefficient
x7(x−2x5)=0
Separate the equation into 2 possible cases
x7=0x−2x5=0
The only way a power can be 0 is when the base equals 0
x=0x−2x5=0
Solve the equation
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Evaluate
x−2x5=0
Factor the expression
x(1−2x4)=0
Separate the equation into 2 possible cases
x=01−2x4=0
Solve the equation
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Evaluate
1−2x4=0
Move the constant to the right-hand side and change its sign
−2x4=0−1
Removing 0 doesn't change the value,so remove it from the expression
−2x4=−1
Change the signs on both sides of the equation
2x4=1
Divide both sides
22x4=21
Divide the numbers
x4=21
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±421
Simplify the expression
x=±248
Separate the equation into 2 possible cases
x=248x=−248
x=0x=248x=−248
x=0x=0x=248x=−248
Find the union
x=0x=248x=−248
Solution
x1=−248,x2=0,x3=248
Alternative Form
x1≈−0.840896,x2=0,x3≈0.840896
Show Solution
