Question
Simplify the expression
27d3−1
Evaluate
d3×27−1
Solution
27d3−1
Show Solution

Factor the expression
(3d−1)(9d2+3d+1)
Evaluate
d3×27−1
Use the commutative property to reorder the terms
27d3−1
Rewrite the expression in exponential form
(3d)3−13
Use a3−b3=(a−b)(a2+ab+b2) to factor the expression
(3d−1)((3d)2+3d×1+12)
Evaluate
More Steps

Evaluate
(3d)2
To raise a product to a power,raise each factor to that power
32d2
Evaluate the power
9d2
(3d−1)(9d2+3d×1+12)
Any expression multiplied by 1 remains the same
(3d−1)(9d2+3d+12)
Solution
(3d−1)(9d2+3d+1)
Show Solution

Find the roots
d=31
Alternative Form
d=0.3˙
Evaluate
d3×27−1
To find the roots of the expression,set the expression equal to 0
d3×27−1=0
Use the commutative property to reorder the terms
27d3−1=0
Move the constant to the right-hand side and change its sign
27d3=0+1
Removing 0 doesn't change the value,so remove it from the expression
27d3=1
Divide both sides
2727d3=271
Divide the numbers
d3=271
Take the 3-th root on both sides of the equation
3d3=3271
Calculate
d=3271
Solution
More Steps

Evaluate
3271
To take a root of a fraction,take the root of the numerator and denominator separately
32731
Simplify the radical expression
3271
Simplify the radical expression
More Steps

Evaluate
327
Write the number in exponential form with the base of 3
333
Reduce the index of the radical and exponent with 3
3
31
d=31
Alternative Form
d=0.3˙
Show Solution
