Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
r5−r3
Evaluate
1×r5−r2×1×r
Any expression multiplied by 1 remains the same
r5−r2×1×r
Solution
More Steps
Multiply the terms
r2×1×r
Rewrite the expression
r2×r
Use the product rule an×am=an+m to simplify the expression
r2+1
Add the numbers
r3
r5−r3
Show Solution
Factor the expression
r3(r−1)(r+1)
Evaluate
1×r5−r2×1×r
Any expression multiplied by 1 remains the same
r5−r2×1×r
Evaluate
More Steps
Evaluate
r2×1×r
Rewrite the expression
r2×r
Use the product rule an×am=an+m to simplify the expression
r2+1
Add the numbers
r3
r5−r3
Factor out r3 from the expression
r3(r2−1)
Solution
More Steps
Evaluate
r2−1
Rewrite the expression in exponential form
r2−12
Use a2−b2=(a−b)(a+b) to factor the expression
(r−1)(r+1)
r3(r−1)(r+1)
Show Solution
Find the roots
r1=−1,r2=0,r3=1
Evaluate
1×r5−r2×1×r
To find the roots of the expression,set the expression equal to 0
1×r5−r2×1×r=0
Any expression multiplied by 1 remains the same
r5−r2×1×r=0
Multiply the terms
More Steps
Multiply the terms
r2×1×r
Rewrite the expression
r2×r
Use the product rule an×am=an+m to simplify the expression
r2+1
Add the numbers
r3
r5−r3=0
Factor the expression
r3(r2−1)=0
Separate the equation into 2 possible cases
r3=0r2−1=0
The only way a power can be 0 is when the base equals 0
r=0r2−1=0
Solve the equation
More Steps
Evaluate
r2−1=0
Move the constant to the right-hand side and change its sign
r2=0+1
Removing 0 doesn't change the value,so remove it from the expression
r2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
r=±1
Simplify the expression
r=±1
Separate the equation into 2 possible cases
r=1r=−1
r=0r=1r=−1
Solution
r1=−1,r2=0,r3=1
Show Solution