Using factor theorem, Show that (a – b) is the factor of a (b²- c²) +b (c²-a²) + c (a²-b²) Answer Plzzz

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Math Margaret 5 months 2022-01-06T01:23:29+00:00 2022-01-06T01:23:29+00:00 1 Answer 0 views 0

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Captcha* 18:9+8+9*3-7:3-1*13 = ? ( )

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Maya · Answer 1 · 2022-01-06T01:24:58+00:00

Maya

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2022-01-06T01:24:58+00:00 January 6, 2022 at 1:24 am

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Answer:

a(b²-c²)+b(c²-a²)+c(a²-b²)

=ab²-ac²+bc²-a²b+a²c-b²c

=ab²-a²b-ac²+bc²+a²c-b²c

=ab(b-a)-c²(a-b)+c(a²-b²)

=-ab(a-b)-c²(a-b)+c((a+b)(a-b))

=(a-b)[-ab-c²+c(a+b)]

=(a-b)[-ab+cb-c²+ac]

=(a-b)[-b(c-a)-c(c-a)]

=(a-b)(b-c)(c-a)