Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
8x−2x3
Evaluate
2x(4−x2)
Apply the distributive property
2x×4−2x×x2
Multiply the numbers
8x−2x×x2
Solution
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
8x−2x3
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Factor the expression
2x(2−x)(2+x)
Evaluate
2x(4−x2)
Solution
2x(2−x)(2+x)
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Find the roots
x1=−2,x2=0,x3=2
Evaluate
2x(4−x2)
To find the roots of the expression,set the expression equal to 0
2x(4−x2)=0
Elimination the left coefficient
x(4−x2)=0
Separate the equation into 2 possible cases
x=04−x2=0
Solve the equation
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Evaluate
4−x2=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
Change the signs on both sides of the equation
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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