Question
Simplify the expression
−80p3−5
Evaluate
20p3−25p2×4p−5
Multiply
More Steps

Multiply the terms
−25p2×4p
Multiply the terms
−100p2×p
Multiply the terms with the same base by adding their exponents
−100p2+1
Add the numbers
−100p3
20p3−100p3−5
Solution
More Steps

Evaluate
20p3−100p3
Collect like terms by calculating the sum or difference of their coefficients
(20−100)p3
Subtract the numbers
−80p3
−80p3−5
Show Solution

Factor the expression
−5(16p3+1)
Evaluate
20p3−25p2×4p−5
Multiply
More Steps

Multiply the terms
25p2×4p
Multiply the terms
100p2×p
Multiply the terms with the same base by adding their exponents
100p2+1
Add the numbers
100p3
20p3−100p3−5
Subtract the terms
More Steps

Simplify
20p3−100p3
Collect like terms by calculating the sum or difference of their coefficients
(20−100)p3
Subtract the numbers
−80p3
−80p3−5
Solution
−5(16p3+1)
Show Solution

Find the roots
p=−434
Alternative Form
p≈−0.39685
Evaluate
20p3−25p2×4p−5
To find the roots of the expression,set the expression equal to 0
20p3−25p2×4p−5=0
Multiply
More Steps

Multiply the terms
25p2×4p
Multiply the terms
100p2×p
Multiply the terms with the same base by adding their exponents
100p2+1
Add the numbers
100p3
20p3−100p3−5=0
Subtract the terms
More Steps

Simplify
20p3−100p3
Collect like terms by calculating the sum or difference of their coefficients
(20−100)p3
Subtract the numbers
−80p3
−80p3−5=0
Move the constant to the right-hand side and change its sign
−80p3=0+5
Removing 0 doesn't change the value,so remove it from the expression
−80p3=5
Change the signs on both sides of the equation
80p3=−5
Divide both sides
8080p3=80−5
Divide the numbers
p3=80−5
Divide the numbers
More Steps

Evaluate
80−5
Cancel out the common factor 5
16−1
Use b−a=−ba=−ba to rewrite the fraction
−161
p3=−161
Take the 3-th root on both sides of the equation
3p3=3−161
Calculate
p=3−161
Solution
More Steps

Evaluate
3−161
An odd root of a negative radicand is always a negative
−3161
To take a root of a fraction,take the root of the numerator and denominator separately
−31631
Simplify the radical expression
−3161
Simplify the radical expression
More Steps

Evaluate
316
Write the expression as a product where the root of one of the factors can be evaluated
38×2
Write the number in exponential form with the base of 2
323×2
The root of a product is equal to the product of the roots of each factor
323×32
Reduce the index of the radical and exponent with 3
232
−2321
Multiply by the Conjugate
232×322−322
Simplify
232×322−34
Multiply the numbers
More Steps

Evaluate
232×322
Multiply the terms
2×2
Multiply the numbers
4
4−34
Calculate
−434
p=−434
Alternative Form
p≈−0.39685
Show Solution
