Question
Simplify the expression
−408y3−18
Evaluate
24y3−16y2×27y−18
Multiply
More Steps

Multiply the terms
−16y2×27y
Multiply the terms
−432y2×y
Multiply the terms with the same base by adding their exponents
−432y2+1
Add the numbers
−432y3
24y3−432y3−18
Solution
More Steps

Evaluate
24y3−432y3
Collect like terms by calculating the sum or difference of their coefficients
(24−432)y3
Subtract the numbers
−408y3
−408y3−18
Show Solution

Factor the expression
−6(68y3+3)
Evaluate
24y3−16y2×27y−18
Multiply
More Steps

Multiply the terms
16y2×27y
Multiply the terms
432y2×y
Multiply the terms with the same base by adding their exponents
432y2+1
Add the numbers
432y3
24y3−432y3−18
Subtract the terms
More Steps

Simplify
24y3−432y3
Collect like terms by calculating the sum or difference of their coefficients
(24−432)y3
Subtract the numbers
−408y3
−408y3−18
Solution
−6(68y3+3)
Show Solution

Find the roots
y=−3431734
Alternative Form
y≈−0.353349
Evaluate
24y3−16y2×27y−18
To find the roots of the expression,set the expression equal to 0
24y3−16y2×27y−18=0
Multiply
More Steps

Multiply the terms
16y2×27y
Multiply the terms
432y2×y
Multiply the terms with the same base by adding their exponents
432y2+1
Add the numbers
432y3
24y3−432y3−18=0
Subtract the terms
More Steps

Simplify
24y3−432y3
Collect like terms by calculating the sum or difference of their coefficients
(24−432)y3
Subtract the numbers
−408y3
−408y3−18=0
Move the constant to the right-hand side and change its sign
−408y3=0+18
Removing 0 doesn't change the value,so remove it from the expression
−408y3=18
Change the signs on both sides of the equation
408y3=−18
Divide both sides
408408y3=408−18
Divide the numbers
y3=408−18
Divide the numbers
More Steps

Evaluate
408−18
Cancel out the common factor 6
68−3
Use b−a=−ba=−ba to rewrite the fraction
−683
y3=−683
Take the 3-th root on both sides of the equation
3y3=3−683
Calculate
y=3−683
Solution
More Steps

Evaluate
3−683
An odd root of a negative radicand is always a negative
−3683
To take a root of a fraction,take the root of the numerator and denominator separately
−36833
Multiply by the Conjugate
368×3682−33×3682
Simplify
368×3682−33×23578
Multiply the numbers
More Steps

Evaluate
−33×23578
Multiply the terms
−31734×2
Use the commutative property to reorder the terms
−231734
368×3682−231734
Multiply the numbers
More Steps

Evaluate
368×3682
The product of roots with the same index is equal to the root of the product
368×682
Calculate the product
3683
Reduce the index of the radical and exponent with 3
68
68−231734
Cancel out the common factor 2
34−31734
Calculate
−3431734
y=−3431734
Alternative Form
y≈−0.353349
Show Solution
