Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x4−4x3+4x2
Evaluate
(x−2)x2(x−2)
Multiply the first two terms
x2(x−2)(x−2)
Multiply the terms
x2(x−2)2
Expand the expression
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Evaluate
(x−2)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×2+22
Calculate
x2−4x+4
x2(x2−4x+4)
Apply the distributive property
x2×x2−x2×4x+x2×4
Multiply the terms
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Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
x4−x2×4x+x2×4
Multiply the terms
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Evaluate
x2×4x
Use the commutative property to reorder the terms
4x2×x
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
4x3
x4−4x3+x2×4
Solution
x4−4x3+4x2
Show Solution
Find the roots
x1=0,x2=2
Evaluate
(x−2)(x2)(x−2)
To find the roots of the expression,set the expression equal to 0
(x−2)(x2)(x−2)=0
Calculate
(x−2)x2(x−2)=0
Multiply the terms
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Multiply the terms
(x−2)x2(x−2)
Multiply the first two terms
x2(x−2)(x−2)
Multiply the terms
x2(x−2)2
x2(x−2)2=0
Separate the equation into 2 possible cases
x2=0(x−2)2=0
The only way a power can be 0 is when the base equals 0
x=0(x−2)2=0
Solve the equation
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Evaluate
(x−2)2=0
The only way a power can be 0 is when the base equals 0
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=0x=2
Solution
x1=0,x2=2
Show Solution