Question

multiplication of (a+b+c)(b+c-a)(c+a-b)(a+b-c)​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

(a+b+c)(b+c-a)(c+a-b)(a+b-c)

=(axb+axc-a²+b²+bxc-axb+cxb+c²-ac)(cxa+cxb-c²+a²+axb-axc-bxa-bxb+bxc)

=(ab+ac-a²+b²+bc-ab+bc+c²-ac)(ac+bc-c²+a²+ab-ac-ab-b²+bc)

=(ab-ab+ac-ac-a²+b²+bc+bc+c²)(ac-ac+bc+bc-c²+a²+ab-ab-b²)

= (-a²+b²+2bc+c²)(2bc-c²-b²+a²)

=(-a²)x2bc+(-a²)x(-c²)+(-a²)x(-b²)+(-a²)xa²+b²x2bc-b²xc²-b²xb²+b²xa²+2bcx2bc-2bcxc²-2bcxb²+2bcxa²+c²x2bc-c²xc²-c²xb²+c²xa²

= -2a²bc+a²c²+a²b²+a⁴+2b³c-b²c²-b⁴+a²b²+4b²c²-2bc³-2b³c +2a²bc+2bc³-c⁴-b²c²+a²c²

=-2a²bc+2a²bc+a²c²+a²c²+a²b²+a²b²+a⁴+2b³c-2b³c-b²c²-b²c² -b⁴+4b²c²-2bc³+2bc³-c⁴

=4a²bc+2a²c²+2a²b²+a⁴-2b²c²-b⁴+4b²c²-c⁴