Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
10x4−40x2
Evaluate
(2x2−8)(x2×5)
Remove the parentheses
(2x2−8)x2×5
Use the commutative property to reorder the terms
(2x2−8)×5x2
Multiply the terms
5x2(2x2−8)
Apply the distributive property
5x2×2x2−5x2×8
Multiply the terms
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Evaluate
5x2×2x2
Multiply the numbers
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
10x4−5x2×8
Solution
10x4−40x2
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Factor the expression
10x2(x−2)(x+2)
Evaluate
(2x2−8)(x2×5)
Remove the parentheses
(2x2−8)x2×5
Use the commutative property to reorder the terms
(2x2−8)×5x2
Multiply the terms
5x2(2x2−8)
Use a2−b2=(a−b)(a+b) to factor the expression
5x2×2(x−2)(x+2)
Solution
10x2(x−2)(x+2)
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Find the roots
x1=−2,x2=0,x3=2
Evaluate
(2x2−8)(x2×5)
To find the roots of the expression,set the expression equal to 0
(2x2−8)(x2×5)=0
Use the commutative property to reorder the terms
(2x2−8)×5x2=0
Multiply the terms
5x2(2x2−8)=0
Elimination the left coefficient
x2(2x2−8)=0
Separate the equation into 2 possible cases
x2=02x2−8=0
The only way a power can be 0 is when the base equals 0
x=02x2−8=0
Solve the equation
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Evaluate
2x2−8=0
Move the constant to the right-hand side and change its sign
2x2=0+8
Removing 0 doesn't change the value,so remove it from the expression
2x2=8
Divide both sides
22x2=28
Divide the numbers
x2=28
Divide the numbers
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Evaluate
28
Reduce the numbers
14
Calculate
4
x2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4
Simplify the expression
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Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
x=±2
Separate the equation into 2 possible cases
x=2x=−2
x=0x=2x=−2
Solution
x1=−2,x2=0,x3=2
Show Solution