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Factorise: p4– 81

  • a)
    (p – 3) (p + 3) (p2+ 9)

  • b)
    (p + 3) (p2+ 9)

  • c)
    (p – 3) (p + 3)

  • d)
    none of these

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Factorise: p4– 81a)(p – 3) (p + 3) (p2+9)b)(p + 3) (p2+9)c...
We have  p4 - 81 = (p2)2 - (9)2 


 


Now using a2 - b2 = (a + b)(a - b), we have


 


         (p2)2 - (9)2 = (p2 + 9)(p2 -9)


 


We can factorise p2 - 9  further as


              p2 - 9 = (p)2 - (3)2


 


                       = (p + 3)(p - 3)


 


∴           p4 - 81 = (p + 3)(p - 3)(p2 + 9)
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Most Upvoted Answer
Factorise: p4– 81a)(p – 3) (p + 3) (p2+9)b)(p + 3) (p2+9)c...
P4 cannot be factorised any further as it is already in its simplest form.
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Community Answer
Factorise: p4– 81a)(p – 3) (p + 3) (p2+9)b)(p + 3) (p2+9)c...
D) option simply open it like other questions
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