Question
Factor the expression
8(t−4)(t+4)
Evaluate
8t2−128
Factor out 8 from the expression
8(t2−16)
Solution
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Evaluate
t2−16
Rewrite the expression in exponential form
t2−42
Use a2−b2=(a−b)(a+b) to factor the expression
(t−4)(t+4)
8(t−4)(t+4)
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Find the roots
t1=−4,t2=4
Evaluate
8t2−128
To find the roots of the expression,set the expression equal to 0
8t2−128=0
Move the constant to the right-hand side and change its sign
8t2=0+128
Removing 0 doesn't change the value,so remove it from the expression
8t2=128
Divide both sides
88t2=8128
Divide the numbers
t2=8128
Divide the numbers
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Evaluate
8128
Reduce the numbers
116
Calculate
16
t2=16
Take the root of both sides of the equation and remember to use both positive and negative roots
t=±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
t=±4
Separate the equation into 2 possible cases
t=4t=−4
Solution
t1=−4,t2=4
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