Question
Simplify the expression
8x6−8
Evaluate
x3×4x2×2x−8
Solution
More Steps

Evaluate
x3×4x2×2x
Multiply the terms with the same base by adding their exponents
x3+2+1×4×2
Add the numbers
x6×4×2
Multiply the terms
x6×8
Use the commutative property to reorder the terms
8x6
8x6−8
Show Solution

Factor the expression
8(x−1)(x2+x+1)(x+1)(x2−x+1)
Evaluate
x3×4x2×2x−8
Evaluate
More Steps

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

Evaluate
x6−1
Rewrite the expression in exponential form
(x3)2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(x3−1)(x3+1)
8(x3−1)(x3+1)
Evaluate
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Evaluate
x3−1
Rewrite the expression in exponential form
x3−13
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(x−1)(x2+x×1+12)
Any expression multiplied by 1 remains the same
(x−1)(x2+x+12)
1 raised to any power equals to 1
(x−1)(x2+x+1)
8(x−1)(x2+x+1)(x3+1)
Solution
More Steps

Evaluate
x3+1
Rewrite the expression in exponential form
x3+13
Use a3+b3=(a+b)(a2−ab+b2) to factor the expression
(x+1)(x2−x×1+12)
Any expression multiplied by 1 remains the same
(x+1)(x2−x+12)
1 raised to any power equals to 1
(x+1)(x2−x+1)
8(x−1)(x2+x+1)(x+1)(x2−x+1)
Show Solution

Find the roots
x1=−1,x2=1
Evaluate
x3×4x2×2x−8
To find the roots of the expression,set the expression equal to 0
x3×4x2×2x−8=0
Multiply
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Multiply the terms
x3×4x2×2x
Multiply the terms with the same base by adding their exponents
x3+2+1×4×2
Add the numbers
x6×4×2
Multiply the terms
x6×8
Use the commutative property to reorder the terms
8x6
8x6−8=0
Move the constant to the right-hand side and change its sign
8x6=0+8
Removing 0 doesn't change the value,so remove it from the expression
8x6=8
Divide both sides
88x6=88
Divide the numbers
x6=88
Divide the numbers
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Evaluate
88
Reduce the numbers
11
Calculate
1
x6=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±61
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
Solution
x1=−1,x2=1
Show Solution
