Question
Factor the expression
(p−3)(p+3)(p2+9)
Evaluate
p4−81
Rewrite the expression in exponential form
(p2)2−(8121)2
Use a2−b2=(a−b)(a+b) to factor the expression
(p2−8121)(p2+8121)
Evaluate
More Steps

Evaluate
p2−8121
Calculate
More Steps

Evaluate
−8121
Rewrite in exponential form
−(34)21
Multiply the exponents
−34×21
Multiply the exponents
−32
Evaluate the power
−9
p2−9
(p2−9)(p2+8121)
Evaluate
More Steps

Evaluate
p2+8121
Calculate
More Steps

Evaluate
8121
Rewrite in exponential form
(34)21
Multiply the exponents
34×21
Multiply the exponents
32
Evaluate the power
9
p2+9
(p2−9)(p2+9)
Solution
More Steps

Evaluate
p2−9
Rewrite the expression in exponential form
p2−32
Use a2−b2=(a−b)(a+b) to factor the expression
(p−3)(p+3)
(p−3)(p+3)(p2+9)
Show Solution

Find the roots
p1=−3,p2=3
Evaluate
p4−81
To find the roots of the expression,set the expression equal to 0
p4−81=0
Move the constant to the right-hand side and change its sign
p4=0+81
Removing 0 doesn't change the value,so remove it from the expression
p4=81
Take the root of both sides of the equation and remember to use both positive and negative roots
p=±481
Simplify the expression
More Steps

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
p=±3
Separate the equation into 2 possible cases
p=3p=−3
Solution
p1=−3,p2=3
Show Solution
