Question
Simplify the expression
180t4−324t5
Evaluate
(5t−9t2)×12×3t3
Multiply the terms
(5t−9t2)×36t3
Multiply the terms
36t3(5t−9t2)
Apply the distributive property
36t3×5t−36t3×9t2
Multiply the terms
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Evaluate
36t3×5t
Multiply the numbers
180t3×t
Multiply the terms
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Evaluate
t3×t
Use the product rule an×am=an+m to simplify the expression
t3+1
Add the numbers
t4
180t4
180t4−36t3×9t2
Solution
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Evaluate
36t3×9t2
Multiply the numbers
324t3×t2
Multiply the terms
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Evaluate
t3×t2
Use the product rule an×am=an+m to simplify the expression
t3+2
Add the numbers
t5
324t5
180t4−324t5
Show Solution

Factor the expression
36t4(5−9t)
Evaluate
(5t−9t2)×12×3t3
Multiply the terms
(5t−9t2)×36t3
Multiply the terms
36t3(5t−9t2)
Factor the expression
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Evaluate
5t−9t2
Rewrite the expression
t×5−t×9t
Factor out t from the expression
t(5−9t)
36t3×t(5−9t)
Solution
36t4(5−9t)
Show Solution

Find the roots
t1=0,t2=95
Alternative Form
t1=0,t2=0.5˙
Evaluate
(5t−9t2)×12(3t3)
To find the roots of the expression,set the expression equal to 0
(5t−9t2)×12(3t3)=0
Multiply the terms
(5t−9t2)×12×3t3=0
Multiply the terms
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Multiply the terms
(5t−9t2)×12×3t3
Multiply the terms
(5t−9t2)×36t3
Multiply the terms
36t3(5t−9t2)
36t3(5t−9t2)=0
Elimination the left coefficient
t3(5t−9t2)=0
Separate the equation into 2 possible cases
t3=05t−9t2=0
The only way a power can be 0 is when the base equals 0
t=05t−9t2=0
Solve the equation
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Evaluate
5t−9t2=0
Factor the expression
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Evaluate
5t−9t2
Rewrite the expression
t×5−t×9t
Factor out t from the expression
t(5−9t)
t(5−9t)=0
When the product of factors equals 0,at least one factor is 0
t=05−9t=0
Solve the equation for t
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Evaluate
5−9t=0
Move the constant to the right-hand side and change its sign
−9t=0−5
Removing 0 doesn't change the value,so remove it from the expression
−9t=−5
Change the signs on both sides of the equation
9t=5
Divide both sides
99t=95
Divide the numbers
t=95
t=0t=95
t=0t=0t=95
Find the union
t=0t=95
Solution
t1=0,t2=95
Alternative Form
t1=0,t2=0.5˙
Show Solution
