Question
Simplify the expression
4x4−29x2+25
Evaluate
(x2−1)(4x2−25)
Apply the distributive property
x2×4x2−x2×25−4x2−(−25)
Multiply the terms
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Evaluate
x2×4x2
Use the commutative property to reorder the terms
4x2×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
4x4
4x4−x2×25−4x2−(−25)
Use the commutative property to reorder the terms
4x4−25x2−4x2−(−25)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4x4−25x2−4x2+25
Solution
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Evaluate
−25x2−4x2
Collect like terms by calculating the sum or difference of their coefficients
(−25−4)x2
Subtract the numbers
−29x2
4x4−29x2+25
Show Solution

Factor the expression
(x−1)(x+1)(2x−5)(2x+5)
Evaluate
(x2−1)(4x2−25)
Use a2−b2=(a−b)(a+b) to factor the expression
(x−1)(x+1)(4x2−25)
Solution
(x−1)(x+1)(2x−5)(2x+5)
Show Solution

Find the roots
x1=−25,x2=−1,x3=1,x4=25
Alternative Form
x1=−2.5,x2=−1,x3=1,x4=2.5
Evaluate
(x2−1)(4x2−25)
To find the roots of the expression,set the expression equal to 0
(x2−1)(4x2−25)=0
Separate the equation into 2 possible cases
x2−1=04x2−25=0
Solve the equation
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Evaluate
x2−1=0
Move the constant to the right-hand side and change its sign
x2=0+1
Removing 0 doesn't change the value,so remove it from the expression
x2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±1
Simplify the expression
x=±1
Separate the equation into 2 possible cases
x=1x=−1
x=1x=−14x2−25=0
Solve the equation
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Evaluate
4x2−25=0
Move the constant to the right-hand side and change its sign
4x2=0+25
Removing 0 doesn't change the value,so remove it from the expression
4x2=25
Divide both sides
44x2=425
Divide the numbers
x2=425
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±425
Simplify the expression
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Evaluate
425
To take a root of a fraction,take the root of the numerator and denominator separately
425
Simplify the radical expression
45
Simplify the radical expression
25
x=±25
Separate the equation into 2 possible cases
x=25x=−25
x=1x=−1x=25x=−25
Solution
x1=−25,x2=−1,x3=1,x4=25
Alternative Form
x1=−2.5,x2=−1,x3=1,x4=2.5
Show Solution
