Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
8n4−16n3−16n2
Evaluate
4n2(2n2−4n−4)
Apply the distributive property
4n2×2n2−4n2×4n−4n2×4
Multiply the terms
More Steps
Evaluate
4n2×2n2
Multiply the numbers
8n2×n2
Multiply the terms
More Steps
Evaluate
n2×n2
Use the product rule an×am=an+m to simplify the expression
n2+2
Add the numbers
n4
8n4
8n4−4n2×4n−4n2×4
Multiply the terms
More Steps
Evaluate
4n2×4n
Multiply the numbers
16n2×n
Multiply the terms
More Steps
Evaluate
n2×n
Use the product rule an×am=an+m to simplify the expression
n2+1
Add the numbers
n3
16n3
8n4−16n3−4n2×4
Solution
8n4−16n3−16n2
Show Solution
Factor the expression
8n2(n2−2n−2)
Evaluate
4n2(2n2−4n−4)
Factor the expression
4n2×2(n2−2n−2)
Solution
8n2(n2−2n−2)
Show Solution
Find the roots
n1=1−3,n2=0,n3=1+3
Alternative Form
n1≈−0.732051,n2=0,n3≈2.732051
Evaluate
(4n2)(2n2−4n−4)
To find the roots of the expression,set the expression equal to 0
(4n2)(2n2−4n−4)=0
Multiply the terms
4n2(2n2−4n−4)=0
Elimination the left coefficient
n2(2n2−4n−4)=0
Separate the equation into 2 possible cases
n2=02n2−4n−4=0
The only way a power can be 0 is when the base equals 0
n=02n2−4n−4=0
Solve the equation
More Steps
Evaluate
2n2−4n−4=0
Substitute a=2,b=−4 and c=−4 into the quadratic formula n=2a−b±b2−4ac
n=2×24±(−4)2−4×2(−4)
Simplify the expression
n=44±(−4)2−4×2(−4)
Simplify the expression
More Steps
Evaluate
(−4)2−4×2(−4)
Multiply
(−4)2−(−32)
Rewrite the expression
42−(−32)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
42+32
Evaluate the power
16+32
Add the numbers
48
n=44±48
Simplify the radical expression
More Steps
Evaluate
48
Write the expression as a product where the root of one of the factors can be evaluated
16×3
Write the number in exponential form with the base of 4
42×3
The root of a product is equal to the product of the roots of each factor
42×3
Reduce the index of the radical and exponent with 2
43
n=44±43
Separate the equation into 2 possible cases
n=44+43n=44−43
Simplify the expression
n=1+3n=44−43
Simplify the expression
n=1+3n=1−3
n=0n=1+3n=1−3
Solution
n1=1−3,n2=0,n3=1+3
Alternative Form
n1≈−0.732051,n2=0,n3≈2.732051
Show Solution