Question

factorize p^4+4 if you can ​

Answer 1

Answer:

answer for the given problem is given

Using Identities

(a+b)^2=a^2+2ab+b^2

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

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

1.

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

2.

${a}^{2} - {b}^{2} = ( a + b\: )( a - b\: )$

TO FACTORISE

${p}^{4} + 4$

EVALUATION

${p}^{4} + 4$

$= {( \: {p}^{2} ) }^{2} + {(2)}^{2}$

$= {( {p}^{2} + 2) }^{2} - 2 \times {p}^{2} \times 2$

$= {( {p}^{2} + 2) }^{2} - 4 {p}^{2}$

$= {( {p}^{2} + 2) }^{2} - {(2p)}^{2}$

$= ( {p}^{2} + 2 + 2p) ( {p}^{2} + 2 - 2p)$

$= ( {p}^{2} + 2p + 2) ( {p}^{2} - 2p + 2)$

RESULT

$\boxed{ \: {p}^{4} + 4 = ( {p}^{2} + 2p + 2) ( {p}^{2} - 2p + 2) \: }$