Question
Factor the expression
(t−2)(t+2)(t2+4)
Evaluate
t4−16
Rewrite the expression in exponential form
(t2)2−(1621)2
Use a2−b2=(a−b)(a+b) to factor the expression
(t2−1621)(t2+1621)
Evaluate
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Evaluate
t2−1621
Calculate
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Evaluate
−1621
Rewrite in exponential form
−(24)21
Multiply the exponents
−24×21
Multiply the exponents
−22
Evaluate the power
−4
t2−4
(t2−4)(t2+1621)
Evaluate
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Evaluate
t2+1621
Calculate
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Evaluate
1621
Rewrite in exponential form
(24)21
Multiply the exponents
24×21
Multiply the exponents
22
Evaluate the power
4
t2+4
(t2−4)(t2+4)
Solution
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Evaluate
t2−4
Rewrite the expression in exponential form
t2−22
Use a2−b2=(a−b)(a+b) to factor the expression
(t−2)(t+2)
(t−2)(t+2)(t2+4)
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Find the roots
t1=−2,t2=2
Evaluate
t4−16
To find the roots of the expression,set the expression equal to 0
t4−16=0
Move the constant to the right-hand side and change its sign
t4=0+16
Removing 0 doesn't change the value,so remove it from the expression
t4=16
Take the root of both sides of the equation and remember to use both positive and negative roots
t=±416
Simplify the expression
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Evaluate
416
Write the number in exponential form with the base of 2
424
Reduce the index of the radical and exponent with 4
2
t=±2
Separate the equation into 2 possible cases
t=2t=−2
Solution
t1=−2,t2=2
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