Question

plz help...................

Answer 1

$\huge\bf\mathfrak{QUESTION \: :}$

Expand using identity :

(p²+16)(p²-(1/4))

$\huge\bf\mathfrak{ANSWER \: :}$

Here

(p²+16)(p²-(1/4))

(p²+16)(p²+(-1/4))

so the identity which will be suitable to solve this question isidentity

(X+a)(X+b)= x²+(a+b)X +ab

so here

X= p²

a= 16

b= -(1/4)

so by applying the identity

we get

(p²+16)(p²+(-1/4))

= (p²)²+(16+(-1/4))p² +(16)(-1/4)

= p⁴ +(((16×4)-1)p²/4) +(-4)

= p⁴+(63p²/4) - 4

also we can write it as

taking (1/4) in common

we get

p⁴+(63p²/4) - 4

= (1/4)(4p⁴+63p²-16)

$\huge\bf\mathfrak{NOTE \: :}$

while solving such questions

you must remember all the identities

and should understand which will be required to Solve the question

Answer 2

Answer: p^4 + 63/4 p^2 - 4

Step-by-step explanation:

$\bold{\Longrightarrow{( p^{2} + 16 )( p^2 - \frac{1}{4})}} \\ \\ \bold{\Longrightarrow{ (p^2 + 16)( p^2 + ( - \frac{1}{4} ))}} \\ \\ \bold{Since\: (a+b)(a+c) = a^2 + ( b + c )a + bc} \\ \\\bold{ Here\: a =p^2\:b=16\:and\:c=-\frac{1}{4} }\\ \\ \bold{= (p^2)^2 + ( 16 - \frac{1}{4} )p^2 -(\frac{1}{4})(16)}\\ \\ \bold{ = p^4 + \frac{63}{4}p^2 - 4}$

Conecpt = Formula used are (a + b)(a + c) and simple mathematical abbrivations. Taking L.C.M and squaring of terms.