Wambach658
Answered



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

(1) (p^2 + 9)(p^2 - 9)

(2) (p^2 - 9)(p^2 - 9)

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

(4) (p + 3)(p - 3)(p + 3)(p - 3)

Verified Answer :

Panoyin

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).

calculista

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

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

Related Questions