Question
Factor the expression
2(x−4)(x+4)
Evaluate
2x2−32
Factor out 2 from the expression
2(x2−16)
Solution
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Evaluate
x2−16
Rewrite the expression in exponential form
x2−42
Use a2−b2=(a−b)(a+b) to factor the expression
(x−4)(x+4)
2(x−4)(x+4)
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Find the roots
x1=−4,x2=4
Evaluate
2x2−32
To find the roots of the expression,set the expression equal to 0
2x2−32=0
Move the constant to the right-hand side and change its sign
2x2=0+32
Removing 0 doesn't change the value,so remove it from the expression
2x2=32
Divide both sides
22x2=232
Divide the numbers
x2=232
Divide the numbers
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Evaluate
232
Reduce the numbers
116
Calculate
16
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
Solution
x1=−4,x2=4
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