Question
Simplify the expression
4x6−4x3
Evaluate
x3(x2×4x−4)
Multiply
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Evaluate
x2×4x
Multiply the terms with the same base by adding their exponents
x2+1×4
Add the numbers
x3×4
Use the commutative property to reorder the terms
4x3
x3(4x3−4)
Apply the distributive property
x3×4x3−x3×4
Multiply the terms
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Evaluate
x3×4x3
Use the commutative property to reorder the terms
4x3×x3
Multiply the terms
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Evaluate
x3×x3
Use the product rule an×am=an+m to simplify the expression
x3+3
Add the numbers
x6
4x6
4x6−x3×4
Solution
4x6−4x3
Show Solution

Factor the expression
4x3(x−1)(x2+x+1)
Evaluate
x3(x2×4x−4)
Multiply
More Steps

Evaluate
x2×4x
Multiply the terms with the same base by adding their exponents
x2+1×4
Add the numbers
x3×4
Use the commutative property to reorder the terms
4x3
x3(4x3−4)
Factor the expression
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Evaluate
4x3−4
Factor out 4 from the expression
4(x3−1)
Factor the expression
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Evaluate
x3−1
Calculate
x3+x2+x−x2−x−1
Rewrite the expression
x×x2+x×x+x−x2−x−1
Factor out x from the expression
x(x2+x+1)−x2−x−1
Factor out −1 from the expression
x(x2+x+1)−(x2+x+1)
Factor out x2+x+1 from the expression
(x−1)(x2+x+1)
4(x−1)(x2+x+1)
x3×4(x−1)(x2+x+1)
Solution
4x3(x−1)(x2+x+1)
Show Solution

Find the roots
x1=0,x2=1
Evaluate
(x3)(x2×4x−4)
To find the roots of the expression,set the expression equal to 0
(x3)(x2×4x−4)=0
Calculate
x3(x2×4x−4)=0
Multiply
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Multiply the terms
x2×4x
Multiply the terms with the same base by adding their exponents
x2+1×4
Add the numbers
x3×4
Use the commutative property to reorder the terms
4x3
x3(4x3−4)=0
Separate the equation into 2 possible cases
x3=04x3−4=0
The only way a power can be 0 is when the base equals 0
x=04x3−4=0
Solve the equation
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Evaluate
4x3−4=0
Move the constant to the right-hand side and change its sign
4x3=0+4
Removing 0 doesn't change the value,so remove it from the expression
4x3=4
Divide both sides
44x3=44
Divide the numbers
x3=44
Divide the numbers
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Evaluate
44
Reduce the numbers
11
Calculate
1
x3=1
Take the 3-th root on both sides of the equation
3x3=31
Calculate
x=31
Simplify the root
x=1
x=0x=1
Solution
x1=0,x2=1
Show Solution
