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algol [13]
2 years ago
10

When factored completely, the expression p^4 - 81 is equivalent to

Mathematics
2 answers:
adelina 88 [10]2 years ago
4 0

we have

p^4 - 81

we know that

(a^{2} -b^{2} )=(a+b)(a-b)

so

(p^4 - 81)=(p^{2} +9)(p^{2} -9) ------> expression 1

and

(p^{2} -9)=(p +3)(p-3) ------> expression 2

Substitute expression 2 in expression 1

(p^4 - 81)=(p^{2} +9)(p+3)(p-3)

therefore

the answer is the option

(p^{2} +9)(p+3)(p-3)

Paha777 [63]2 years ago
3 0
P⁴ - 81
p⁴ + 9p² - 9p² - 81
p²(p²) + p²(9) - 9(p²) - 9(9)
p²(p² + 9) - 9(p² + 9)
(p² - 9)(p² + 9)
(p² + 3p - 3p - 9)(p² + 9)
(p(p) + p(3) - 3(p) - 3(3))(p² + 9)
(p(p + 3) - 3(p + 3))(p² + 9)
(p - 3)(p + 3)(p² + 9)

The answer is (3).
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