How do you multiply (m^2-4mp+p^2)(m^2+4mp-p^2) (m2−4mp+p2)(m2+4mp−p2)?

2 Answers
Alex
Apr 11, 2018

Please look below(I hope I got the algebra right).

Explanation:

(m^2 - 4mp + p^2)(m^2 + 4mp - p^2)(m2−4mp+p2)(m2+4mp−p2)

= m^2(m^2 + 4mp - p^2) - 4mp( m^2 + 4mp - p^2) + p^2(m^2 + 4mp - p^2)=m2(m2+4mp−p2)−4mp(m2+4mp−p2)+p2(m2+4mp−p2)

= m^4 + 4m^3p - p^2m^2 - 4m^3p - 16m^2p^2 + 4mp^3 + p^2m^2 + 4mp^3 - p^4=m4+4m3p−p2m2−4m3p−16m2p2+4mp3+p2m2+4mp3−p4

= m^4-16m^2p^2+8mp^3-p^4=m4−16m2p2+8mp3−p4

Shwetank Mauria
Apr 11, 2018

(m^2 - 4mp + p^2)(m^2 + 4mp - p^2)=m^4-16m^p^2+8mp^3-p^4(m2−4mp+p2)(m2+4mp−p2)=m4−16mp^2+8mp3−p4

Explanation:

One can use formula (a-b)(a+b)=a^2-b^2(a−b)(a+b)=a2−b2 as follows:

(m^2 - 4mp + p^2)(m^2 + 4mp - p^2)(m2−4mp+p2)(m2+4mp−p2)

= (m^2 - (4mp - p^2))((m^2 + (4mp - p^2))(m2−(4mp−p2))((m2+(4mp−p2))

= (m^2)^2-(4mp-p^2)^2(m2)2−(4mp−p2)2

= m^4-(16m^2p^2-8mp^3+p^4)m4−(16m2p2−8mp3+p4)

= m^4-16m^2p^2+8mp^3-p^4m4−16m2p2+8mp3−p4

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