Question

Express 81-p⁴ as the product of three expressions(with the help of formula)​

Answer 1

Answer:

81-p^4

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

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

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

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

Answer 2

Answer:

Hope it helps :)

Step-by-step explanation:

$81 = 3^4$

as we know  $a^2-b^2 = (a+b)(a-b)$

Hence, $a^4-b^4 = (a^2+b^2)(a^2-b^2)$

According to the statements made above we can conclude:

$= 81-p^4\\\\\\=3^4-p^4\\\\\\=(3^2+p^2)(3^2-p^2)\\\\\\=(3^2+p^2)(3+p)(3-p)\\\\\\=(9+p^2)(3+p)(3-p)$

Hope it helps :)