Question
Simplify the expression
16t4−120t3
Evaluate
16t4−24t3−8t2×12t
Multiply
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Multiply the terms
−8t2×12t
Multiply the terms
−96t2×t
Multiply the terms with the same base by adding their exponents
−96t2+1
Add the numbers
−96t3
16t4−24t3−96t3
Solution
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Evaluate
−24t3−96t3
Collect like terms by calculating the sum or difference of their coefficients
(−24−96)t3
Subtract the numbers
−120t3
16t4−120t3
Show Solution

Factor the expression
8t3(2t−15)
Evaluate
16t4−24t3−8t2×12t
Multiply
More Steps

Multiply the terms
8t2×12t
Multiply the terms
96t2×t
Multiply the terms with the same base by adding their exponents
96t2+1
Add the numbers
96t3
16t4−24t3−96t3
Subtract the terms
More Steps

Evaluate
−24t3−96t3
Collect like terms by calculating the sum or difference of their coefficients
(−24−96)t3
Subtract the numbers
−120t3
16t4−120t3
Rewrite the expression
8t3×2t−8t3×15
Solution
8t3(2t−15)
Show Solution

Find the roots
t1=0,t2=215
Alternative Form
t1=0,t2=7.5
Evaluate
16t4−24t3−8t2×12t
To find the roots of the expression,set the expression equal to 0
16t4−24t3−8t2×12t=0
Multiply
More Steps

Multiply the terms
8t2×12t
Multiply the terms
96t2×t
Multiply the terms with the same base by adding their exponents
96t2+1
Add the numbers
96t3
16t4−24t3−96t3=0
Subtract the terms
More Steps

Simplify
16t4−24t3−96t3
Subtract the terms
More Steps

Evaluate
−24t3−96t3
Collect like terms by calculating the sum or difference of their coefficients
(−24−96)t3
Subtract the numbers
−120t3
16t4−120t3
16t4−120t3=0
Factor the expression
8t3(2t−15)=0
Divide both sides
t3(2t−15)=0
Separate the equation into 2 possible cases
t3=02t−15=0
The only way a power can be 0 is when the base equals 0
t=02t−15=0
Solve the equation
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Evaluate
2t−15=0
Move the constant to the right-hand side and change its sign
2t=0+15
Removing 0 doesn't change the value,so remove it from the expression
2t=15
Divide both sides
22t=215
Divide the numbers
t=215
t=0t=215
Solution
t1=0,t2=215
Alternative Form
t1=0,t2=7.5
Show Solution
