Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−16k4+16k3
Evaluate
−4k2(4k2−4k)
Apply the distributive property
−4k2×4k2−(−4k2×4k)
Multiply the terms
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Evaluate
−4k2×4k2
Multiply the numbers
−16k2×k2
Multiply the terms
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Evaluate
k2×k2
Use the product rule an×am=an+m to simplify the expression
k2+2
Add the numbers
k4
−16k4
−16k4−(−4k2×4k)
Multiply the terms
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Evaluate
−4k2×4k
Multiply the numbers
−16k2×k
Multiply the terms
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Evaluate
k2×k
Use the product rule an×am=an+m to simplify the expression
k2+1
Add the numbers
k3
−16k3
−16k4−(−16k3)
Solution
−16k4+16k3
Show Solution
Factor the expression
−16k3(k−1)
Evaluate
−4k2(4k2−4k)
Factor the expression
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Evaluate
4k2−4k
Rewrite the expression
4k×k−4k
Factor out 4k from the expression
4k(k−1)
−4k2×4k(k−1)
Solution
−16k3(k−1)
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Find the roots
k1=0,k2=1
Evaluate
−4k2(4k2−4k)
To find the roots of the expression,set the expression equal to 0
−4k2(4k2−4k)=0
Change the sign
4k2(4k2−4k)=0
Elimination the left coefficient
k2(4k2−4k)=0
Separate the equation into 2 possible cases
k2=04k2−4k=0
The only way a power can be 0 is when the base equals 0
k=04k2−4k=0
Solve the equation
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Evaluate
4k2−4k=0
Factor the expression
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Evaluate
4k2−4k
Rewrite the expression
4k×k−4k
Factor out 4k from the expression
4k(k−1)
4k(k−1)=0
When the product of factors equals 0,at least one factor is 0
4k=0k−1=0
Solve the equation for k
k=0k−1=0
Solve the equation for k
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Evaluate
k−1=0
Move the constant to the right-hand side and change its sign
k=0+1
Removing 0 doesn't change the value,so remove it from the expression
k=1
k=0k=1
k=0k=0k=1
Find the union
k=0k=1
Solution
k1=0,k2=1
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