Question
Simplify the expression
12x13−12x12
Evaluate
(12x−1×x3×24x2)(123x2x3×24x2)
Remove the parentheses
12x−1×x3×24x2×123x2x3×24x2
Cancel out the common factor 3
12x−1×x3×24x2×4x2x3×24x2
Multiply the terms with the same base by adding their exponents
12x−1×x3+2+3+2×24×4x2×24
Add the numbers
12x−1×x10×24×4x2×24
Multiply the terms
12x−1×x10×576×4x2
Multiply the terms
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Multiply the terms
12x−1×x10
Multiply the terms
12(x−1)x10
Multiply the terms
12x10(x−1)
12x10(x−1)×576×4x2
Multiply the terms
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Multiply the terms
12x10(x−1)×576
Cancel out the common factor 12
x10(x−1)×48
Use the commutative property to reorder the terms
48x10(x−1)
48x10(x−1)×4x2
Cancel out the common factor 4
12x10(x−1)x2
Multiply the terms
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Evaluate
x10×x2
Use the product rule an×am=an+m to simplify the expression
x10+2
Add the numbers
x12
12x12(x−1)
Apply the distributive property
12x12×x−12x12×1
Multiply the terms
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Evaluate
x12×x
Use the product rule an×am=an+m to simplify the expression
x12+1
Add the numbers
x13
12x13−12x12×1
Solution
12x13−12x12
Show Solution

Find the roots
x1=0,x2=1
Evaluate
(12x−1×x3×24x2)(123x2x3×24x2)
To find the roots of the expression,set the expression equal to 0
(12x−1×x3×24x2)(123x2x3×24x2)=0
Multiply
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Multiply the terms
12x−1×x3×24x2
Multiply the terms with the same base by adding their exponents
12x−1×x3+2×24
Add the numbers
12x−1×x5×24
Multiply the terms
More Steps

Multiply the terms
12x−1×x5
Multiply the terms
12(x−1)x5
Multiply the terms
12x5(x−1)
12x5(x−1)×24
Cancel out the common factor 12
x5(x−1)×2
Use the commutative property to reorder the terms
2x5(x−1)
2x5(x−1)(123x2x3×24x2)=0
Cancel out the common factor 3
2x5(x−1)(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
2x5(x−1)×6x7=0
Multiply
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Evaluate
2x5(x−1)×6x7
Multiply the terms
12x5(x−1)x7
Multiply the terms
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Evaluate
x5×x7
Use the product rule an×am=an+m to simplify the expression
x5+7
Add the numbers
x12
12x12(x−1)
12x12(x−1)=0
Elimination the left coefficient
x12(x−1)=0
Separate the equation into 2 possible cases
x12=0x−1=0
The only way a power can be 0 is when the base equals 0
x=0x−1=0
Solve the equation
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Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=0x=1
Solution
x1=0,x2=1
Show Solution
