Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−16x3+8x4−x5
Evaluate
(4−x)(x−4)x3
Multiply the first two terms
−(4−x)2x3
Use the commutative property to reorder the terms
−x3(4−x)2
Expand the expression
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Evaluate
(4−x)2
Use (a−b)2=a2−2ab+b2 to expand the expression
42−2×4x+x2
Calculate
16−8x+x2
−x3(16−8x+x2)
Apply the distributive property
−x3×16−(−x3×8x)−x3×x2
Use the commutative property to reorder the terms
−16x3−(−x3×8x)−x3×x2
Multiply the terms
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Evaluate
−x3×8x
Multiply the numbers
−8x3×x
Multiply the terms
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Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
−8x4
−16x3−(−8x4)−x3×x2
Multiply the terms
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Evaluate
x3×x2
Use the product rule an×am=an+m to simplify the expression
x3+2
Add the numbers
x5
−16x3−(−8x4)−x5
Solution
−16x3+8x4−x5
Show Solution
Find the roots
x1=0,x2=4
Evaluate
(4−x)(x−4)(x3)
To find the roots of the expression,set the expression equal to 0
(4−x)(x−4)(x3)=0
Calculate
(4−x)(x−4)x3=0
Multiply the terms
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Multiply the terms
(4−x)(x−4)x3
Multiply the first two terms
−(4−x)2x3
Use the commutative property to reorder the terms
−x3(4−x)2
−x3(4−x)2=0
Change the sign
x3(4−x)2=0
Separate the equation into 2 possible cases
x3=0(4−x)2=0
The only way a power can be 0 is when the base equals 0
x=0(4−x)2=0
Solve the equation
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Evaluate
(4−x)2=0
The only way a power can be 0 is when the base equals 0
4−x=0
Move the constant to the right-hand side and change its sign
−x=0−4
Removing 0 doesn't change the value,so remove it from the expression
−x=−4
Change the signs on both sides of the equation
x=4
x=0x=4
Solution
x1=0,x2=4
Show Solution