Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x3−4x2−16x+64
Evaluate
(x2−16)(x−4)
Apply the distributive property
x2×x−x2×4−16x−(−16×4)
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−x2×4−16x−(−16×4)
Use the commutative property to reorder the terms
x3−4x2−16x−(−16×4)
Multiply the numbers
x3−4x2−16x−(−64)
Solution
x3−4x2−16x+64
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Factor the expression
(x−4)2(x+4)
Evaluate
(x2−16)(x−4)
Use a2−b2=(a−b)(a+b) to factor the expression
(x−4)(x+4)(x−4)
Solution
(x−4)2(x+4)
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Find the roots
x1=−4,x2=4
Evaluate
(x2−16)(x−4)
To find the roots of the expression,set the expression equal to 0
(x2−16)(x−4)=0
Separate the equation into 2 possible cases
x2−16=0x−4=0
Solve the equation
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Evaluate
x2−16=0
Move the constant to the right-hand side and change its sign
x2=0+16
Removing 0 doesn't change the value,so remove it from the expression
x2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±16
Simplify the expression
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Evaluate
16
Write the number in exponential form with the base of 4
42
Reduce the index of the radical and exponent with 2
4
x=±4
Separate the equation into 2 possible cases
x=4x=−4
x=4x=−4x−4=0
Solve the equation
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Evaluate
x−4=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
x=4x=−4x=4
Find the union
x=4x=−4
Solution
x1=−4,x2=4
Show Solution