Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
2n−1
Evaluate
n2−(n−1)2
Expand the expression
n2−n2+2n−1
The sum of two opposites equals 0
More Steps
Evaluate
n2−n2
Collect like terms
(1−1)n2
Add the coefficients
0×n2
Calculate
0
0+2n−1
Solution
2n−1
Show Solution
Factor the expression
2n−1
Evaluate
n2−(n−1)2
Use a2−b2=(a−b)(a+b) to factor the expression
(n−(n−1))(n+n−1)
Evaluate
More Steps
Evaluate
n−(n−1)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
n−n+1
The sum of two opposites equals 0
More Steps
Evaluate
n−n
Collect like terms
(1−1)n
Add the coefficients
0×n
Calculate
0
0+1
Remove 0
1
1×(n+n−1)
Evaluate
More Steps
Evaluate
n+n−1
Add the terms
More Steps
Evaluate
n+n
Collect like terms by calculating the sum or difference of their coefficients
(1+1)n
Add the numbers
2n
2n−1
1×(2n−1)
Solution
2n−1
Show Solution
Find the roots
n=21
Alternative Form
n=0.5
Evaluate
n2−(n−1)2
To find the roots of the expression,set the expression equal to 0
n2−(n−1)2=0
Factor the expression
More Steps
Evaluate
n2−(n−1)2
Use a2−b2=(a−b)(a+b) to factor the expression
(n−(n−1))(n+n−1)
Evaluate
More Steps
Evaluate
n−(n−1)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
n−n+1
The sum of two opposites equals 0
0+1
Remove 0
1
1×(n+n−1)
Evaluate
1×(2n−1)
1×(2n−1)=0
Calculate
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=21
Solution
n=21
Alternative Form
n=0.5
Show Solution