Question

81 - p4 factorise using identities and full explanation ​

Answer 1

Answer:

(3²+p²)(3+p)(3-p)

Step-by-step explanation:

81 = 3⁴

Using this, we get,

3⁴ -p⁴

=(3²)² - (p²)²

= (3²+ p²)(3² -p²). [a²-b² = (a+b)(a-b)]

=(3²+ p²)(3+p)(3-p)

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Answer 2

$81 - {p}^{4} \\ 3⁴=81</p><p>so,{3}^{4} - {p}^{4} = ({ {3}^{2} })^{2} - ({ {p}^{2} })^{2}$

${x}^{2} - {y}^{2} = (x - y)(x + y) \\ = ({3}^{2} - {p}^{2} )({3}^{2} + {p}^{2} )$

Again express 3² - p² as above

${3}^{2} - {p}^{2} = (3 - p) + (3 + p)$

$= (3 - p)(3 + p)( {3}^{2} + {p}^{2})$

Hope this will be helpful.