Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−3z3−1
Evaluate
z3−2z2×2z−1
Multiply
More Steps
Multiply the terms
−2z2×2z
Multiply the terms
−4z2×z
Multiply the terms with the same base by adding their exponents
−4z2+1
Add the numbers
−4z3
z3−4z3−1
Solution
More Steps
Evaluate
z3−4z3
Collect like terms by calculating the sum or difference of their coefficients
(1−4)z3
Subtract the numbers
−3z3
−3z3−1
Show Solution
Find the roots
z=−339
Alternative Form
z≈−0.693361
Evaluate
z3−2z2×2z−1
To find the roots of the expression,set the expression equal to 0
z3−2z2×2z−1=0
Multiply
More Steps
Multiply the terms
2z2×2z
Multiply the terms
4z2×z
Multiply the terms with the same base by adding their exponents
4z2+1
Add the numbers
4z3
z3−4z3−1=0
Subtract the terms
More Steps
Simplify
z3−4z3
Collect like terms by calculating the sum or difference of their coefficients
(1−4)z3
Subtract the numbers
−3z3
−3z3−1=0
Move the constant to the right-hand side and change its sign
−3z3=0+1
Removing 0 doesn't change the value,so remove it from the expression
−3z3=1
Change the signs on both sides of the equation
3z3=−1
Divide both sides
33z3=3−1
Divide the numbers
z3=3−1
Use b−a=−ba=−ba to rewrite the fraction
z3=−31
Take the 3-th root on both sides of the equation
3z3=3−31
Calculate
z=3−31
Solution
More Steps
Evaluate
3−31
An odd root of a negative radicand is always a negative
−331
To take a root of a fraction,take the root of the numerator and denominator separately
−3331
Simplify the radical expression
−331
Multiply by the Conjugate
33×332−332
Simplify
33×332−39
Multiply the numbers
More Steps
Evaluate
33×332
The product of roots with the same index is equal to the root of the product
33×32
Calculate the product
333
Reduce the index of the radical and exponent with 3
3
3−39
Calculate
−339
z=−339
Alternative Form
z≈−0.693361
Show Solution