Question
Simplify the expression
Solution
x6−10x4+25x2
Evaluate
(x2−5)2x2
Use the commutative property to reorder the terms
x2(x2−5)2
Expand the expression
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Evaluate
(x2−5)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(x2)2−2x2×5+52
Calculate
x4−10x2+25
x2(x4−10x2+25)
Apply the distributive property
x2×x4−x2×10x2+x2×25
Multiply the terms
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Evaluate
x2×x4
Use the product rule an×am=an+m to simplify the expression
x2+4
Add the numbers
x6
x6−x2×10x2+x2×25
Multiply the terms
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Evaluate
x2×10x2
Use the commutative property to reorder the terms
10x2×x2
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
10x4
x6−10x4+x2×25
Solution
x6−10x4+25x2
Show Solution
Find the roots
Find the roots of the algebra expression
x1=−5,x2=0,x3=5
Alternative Form
x1≈−2.236068,x2=0,x3≈2.236068
Evaluate
(x2−5)2x2
To find the roots of the expression,set the expression equal to 0
(x2−5)2x2=0
Use the commutative property to reorder the terms
x2(x2−5)2=0
Separate the equation into 2 possible cases
x2=0(x2−5)2=0
The only way a power can be 0 is when the base equals 0
x=0(x2−5)2=0
Solve the equation
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Evaluate
(x2−5)2=0
The only way a power can be 0 is when the base equals 0
x2−5=0
Move the constant to the right-hand side and change its sign
x2=0+5
Removing 0 doesn't change the value,so remove it from the expression
x2=5
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±5
Separate the equation into 2 possible cases
x=5x=−5
x=0x=5x=−5
Solution
x1=−5,x2=0,x3=5
Alternative Form
x1≈−2.236068,x2=0,x3≈2.236068
Show Solution