Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
t9−t4
Evaluate
t4×t5−t4
Solution
More Steps
Evaluate
t4×t5
Use the product rule an×am=an+m to simplify the expression
t4+5
Add the numbers
t9
t9−t4
Show Solution
Factor the expression
t4(t−1)(t4+t3+t2+t+1)
Evaluate
t4×t5−t4
Factor out t4 from the expression
t4(t5−1)
Solution
More Steps
Evaluate
t5−1
Calculate
t5+t4+t3+t2+t−t4−t3−t2−t−1
Rewrite the expression
t×t4+t×t3+t×t2+t×t+t−t4−t3−t2−t−1
Factor out t from the expression
t(t4+t3+t2+t+1)−t4−t3−t2−t−1
Factor out −1 from the expression
t(t4+t3+t2+t+1)−(t4+t3+t2+t+1)
Factor out t4+t3+t2+t+1 from the expression
(t−1)(t4+t3+t2+t+1)
t4(t−1)(t4+t3+t2+t+1)
Show Solution
Find the roots
t1=0,t2=1
Evaluate
t4×t5−t4
To find the roots of the expression,set the expression equal to 0
t4×t5−t4=0
Multiply the terms
More Steps
Evaluate
t4×t5
Use the product rule an×am=an+m to simplify the expression
t4+5
Add the numbers
t9
t9−t4=0
Factor the expression
t4(t5−1)=0
Separate the equation into 2 possible cases
t4=0t5−1=0
The only way a power can be 0 is when the base equals 0
t=0t5−1=0
Solve the equation
More Steps
Evaluate
t5−1=0
Move the constant to the right-hand side and change its sign
t5=0+1
Removing 0 doesn't change the value,so remove it from the expression
t5=1
Take the 5-th root on both sides of the equation
5t5=51
Calculate
t=51
Simplify the root
t=1
t=0t=1
Solution
t1=0,t2=1
Show Solution