Question

Factorise using identities:
$p^4–(q+r{)}^4$

• A. $(p+q-r)(p-q+r)[p^2+(q+r{)}^2]$
• B. $(p+q+r{)}^2[p^2+(q+r{)}^2]$
• C. $(p-q-r{)}^2[p^2+(q+r{)}^2]$
• D. $(p-q-r)(p+q+r)[p^2+(q+r{)}^2]$
  

Answer 1

The correct option is D $(p-q-r)(p+q+r)[p^2+(q+r{)}^2]$


$p^4–(q+r{)}^4$

$=(p^2{)}^2-[(q+r{)}^2{]}^2$

$=[p^2-(q+r{)}^2\left]\right[p^2+(q+r{)}^2]$

[Using identity: $a^2-b^2=(a-b)(a+b)$ ]

$=[p-(q+r\left)\right][p+(q+r\left)\right][p^2+(q+r{)}^2]$

$=(p-q-r)(p+q+r)[p^2+(q+r{)}^2]$