Question
Factor the expression
(y−3)(y+3)(y2+9)
Evaluate
y4−81
Rewrite the expression in exponential form
(y2)2−(8121)2
Use a2−b2=(a−b)(a+b) to factor the expression
(y2−8121)(y2+8121)
Evaluate
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Evaluate
y2−8121
Calculate
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Evaluate
−8121
Rewrite in exponential form
−(34)21
Multiply the exponents
−34×21
Multiply the exponents
−32
Evaluate the power
−9
y2−9
(y2−9)(y2+8121)
Evaluate
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Evaluate
y2+8121
Calculate
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Evaluate
8121
Rewrite in exponential form
(34)21
Multiply the exponents
34×21
Multiply the exponents
32
Evaluate the power
9
y2+9
(y2−9)(y2+9)
Solution
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Evaluate
y2−9
Rewrite the expression in exponential form
y2−32
Use a2−b2=(a−b)(a+b) to factor the expression
(y−3)(y+3)
(y−3)(y+3)(y2+9)
Show Solution

Find the roots
y1=−3,y2=3
Evaluate
y4−81
To find the roots of the expression,set the expression equal to 0
y4−81=0
Move the constant to the right-hand side and change its sign
y4=0+81
Removing 0 doesn't change the value,so remove it from the expression
y4=81
Take the root of both sides of the equation and remember to use both positive and negative roots
y=±481
Simplify the expression
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Evaluate
481
Write the number in exponential form with the base of 3
434
Reduce the index of the radical and exponent with 4
3
y=±3
Separate the equation into 2 possible cases
y=3y=−3
Solution
y1=−3,y2=3
Show Solution
