Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
12x4−48x2
Evaluate
3(x2−4)(x2×4)
Remove the parentheses
3(x2−4)x2×4
Multiply the terms
12(x2−4)x2
Multiply the terms
12x2(x2−4)
Apply the distributive property
12x2×x2−12x2×4
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
12x4−12x2×4
Solution
12x4−48x2
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Factor the expression
12x2(x−2)(x+2)
Evaluate
3(x2−4)(x2×4)
Remove the parentheses
3(x2−4)x2×4
Use the commutative property to reorder the terms
3(x2−4)×4x2
Multiply the terms
12(x2−4)x2
Multiply the terms
12x2(x2−4)
Solution
12x2(x−2)(x+2)
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Find the roots
x1=−2,x2=0,x3=2
Evaluate
3(x2−4)(x2×4)
To find the roots of the expression,set the expression equal to 0
3(x2−4)(x2×4)=0
Use the commutative property to reorder the terms
3(x2−4)×4x2=0
Multiply
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Multiply the terms
3(x2−4)×4x2
Multiply the terms
12(x2−4)x2
Multiply the terms
12x2(x2−4)
12x2(x2−4)=0
Elimination the left coefficient
x2(x2−4)=0
Separate the equation into 2 possible cases
x2=0x2−4=0
The only way a power can be 0 is when the base equals 0
x=0x2−4=0
Solve the equation
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Evaluate
x2−4=0
Move the constant to the right-hand side and change its sign
x2=0+4
Removing 0 doesn't change the value,so remove it from the expression
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
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