Question
Simplify the expression
−2x3+16x2−32x
Evaluate
−2x(x−4)(x−4)
Multiply the terms
−2x(x−4)2
Expand the expression
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Evaluate
(x−4)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×4+42
Calculate
x2−8x+16
−2x(x2−8x+16)
Apply the distributive property
−2x×x2−(−2x×8x)−2x×16
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
−2x3−(−2x×8x)−2x×16
Multiply the terms
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Evaluate
−2x×8x
Multiply the numbers
−16x×x
Multiply the terms
−16x2
−2x3−(−16x2)−2x×16
Multiply the numbers
−2x3−(−16x2)−32x
Solution
−2x3+16x2−32x
Show Solution

Find the roots
x1=0,x2=4
Evaluate
−2x(x−4)(x−4)
To find the roots of the expression,set the expression equal to 0
−2x(x−4)(x−4)=0
Multiply the terms
−2x(x−4)2=0
Change the sign
2x(x−4)2=0
Elimination the left coefficient
x(x−4)2=0
Separate the equation into 2 possible cases
x=0(x−4)2=0
Solve the equation
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Evaluate
(x−4)2=0
The only way a power can be 0 is when the base equals 0
x−4=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
x=0x=4
Solution
x1=0,x2=4
Show Solution
