Question
Simplify the expression
62n3+3n2+n
Evaluate
n(n+1)×62n+1
Multiply the terms
6n(2n+1)(n+1)
Multiply the terms
6n(2n+1)(n+1)
Solution
More Steps

Evaluate
n(2n+1)(n+1)
Multiply the terms
More Steps

Evaluate
n(2n+1)
Apply the distributive property
n×2n+n×1
Multiply the terms
2n2+n×1
Any expression multiplied by 1 remains the same
2n2+n
(2n2+n)(n+1)
Apply the distributive property
2n2×n+2n2×1+n×n+n×1
Multiply the terms
More Steps

Evaluate
n2×n
Use the product rule an×am=an+m to simplify the expression
n2+1
Add the numbers
n3
2n3+2n2×1+n×n+n×1
Any expression multiplied by 1 remains the same
2n3+2n2+n×n+n×1
Multiply the terms
2n3+2n2+n2+n×1
Any expression multiplied by 1 remains the same
2n3+2n2+n2+n
Add the terms
More Steps

Evaluate
2n2+n2
Collect like terms by calculating the sum or difference of their coefficients
(2+1)n2
Add the numbers
3n2
2n3+3n2+n
62n3+3n2+n
Show Solution

Find the roots
n1=−1,n2=−21,n3=0
Alternative Form
n1=−1,n2=−0.5,n3=0
Evaluate
n(n+1)×62n+1
To find the roots of the expression,set the expression equal to 0
n(n+1)×62n+1=0
Multiply the terms
More Steps

Multiply the terms
n(n+1)×62n+1
Multiply the terms
6n(2n+1)(n+1)
Multiply the terms
6n(2n+1)(n+1)
6n(2n+1)(n+1)=0
Simplify
n(2n+1)(n+1)=0
Separate the equation into 3 possible cases
n=02n+1=0n+1=0
Solve the equation
More Steps

Evaluate
2n+1=0
Move the constant to the right-hand side and change its sign
2n=0−1
Removing 0 doesn't change the value,so remove it from the expression
2n=−1
Divide both sides
22n=2−1
Divide the numbers
n=2−1
Use b−a=−ba=−ba to rewrite the fraction
n=−21
n=0n=−21n+1=0
Solve the equation
More Steps

Evaluate
n+1=0
Move the constant to the right-hand side and change its sign
n=0−1
Removing 0 doesn't change the value,so remove it from the expression
n=−1
n=0n=−21n=−1
Solution
n1=−1,n2=−21,n3=0
Alternative Form
n1=−1,n2=−0.5,n3=0
Show Solution
