Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
16c4−8c3
Evaluate
2c(2c×1)(4c2−2c×1)
Remove the parentheses
2c×2c×1×(4c2−2c×1)
Multiply the terms
2c×2c×1×(4c2−2c)
Rewrite the expression
2c×2c(4c2−2c)
Multiply the terms
4c×c(4c2−2c)
Multiply the terms
4c2(4c2−2c)
Apply the distributive property
4c2×4c2−4c2×2c
Multiply the terms
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Evaluate
4c2×4c2
Multiply the numbers
16c2×c2
Multiply the terms
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Evaluate
c2×c2
Use the product rule an×am=an+m to simplify the expression
c2+2
Add the numbers
c4
16c4
16c4−4c2×2c
Solution
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Evaluate
4c2×2c
Multiply the numbers
8c2×c
Multiply the terms
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Evaluate
c2×c
Use the product rule an×am=an+m to simplify the expression
c2+1
Add the numbers
c3
8c3
16c4−8c3
Show Solution
Factor the expression
8c3(2c−1)
Evaluate
2c(2c×1)(4c2−2c×1)
Remove the parentheses
2c×2c×1×(4c2−2c×1)
Multiply the terms
2c×2c×1×(4c2−2c)
Multiply the terms
2c×2c(4c2−2c)
Multiply the terms
4c×c(4c2−2c)
Multiply the terms
4c2(4c2−2c)
Factor the expression
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Evaluate
4c2−2c
Rewrite the expression
2c×2c−2c
Factor out 2c from the expression
2c(2c−1)
4c2×2c(2c−1)
Solution
8c3(2c−1)
Show Solution
Find the roots
c1=0,c2=21
Alternative Form
c1=0,c2=0.5
Evaluate
2c(2c×1)(4c2−2c×1)
To find the roots of the expression,set the expression equal to 0
2c(2c×1)(4c2−2c×1)=0
Multiply the terms
2c×2c(4c2−2c×1)=0
Multiply the terms
2c×2c(4c2−2c)=0
Multiply
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Multiply the terms
2c×2c(4c2−2c)
Multiply the terms
4c×c(4c2−2c)
Multiply the terms
4c2(4c2−2c)
4c2(4c2−2c)=0
Elimination the left coefficient
c2(4c2−2c)=0
Separate the equation into 2 possible cases
c2=04c2−2c=0
The only way a power can be 0 is when the base equals 0
c=04c2−2c=0
Solve the equation
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Evaluate
4c2−2c=0
Factor the expression
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Evaluate
4c2−2c
Rewrite the expression
2c×2c−2c
Factor out 2c from the expression
2c(2c−1)
2c(2c−1)=0
When the product of factors equals 0,at least one factor is 0
2c=02c−1=0
Solve the equation for c
c=02c−1=0
Solve the equation for c
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Evaluate
2c−1=0
Move the constant to the right-hand side and change its sign
2c=0+1
Removing 0 doesn't change the value,so remove it from the expression
2c=1
Divide both sides
22c=21
Divide the numbers
c=21
c=0c=21
c=0c=0c=21
Find the union
c=0c=21
Solution
c1=0,c2=21
Alternative Form
c1=0,c2=0.5
Show Solution