A B +5b-5c-ac can be factorised as
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0
Answer:
Let p=b−a and q=c−b so that p+q=b−a+c−b=c−a.
The expression becomes
(a−b)
5
+(b−c)
5
+(c−a)
5
=−p
5
−q
5
+(p+q)
5
=5p
4
q+10p
3
q
2
+10p
2
q
3
+5pq
4
=5pq(p
3
+2p
2
q+2pq
2
+q
3
)
=5pq(p+q)(p
2
+pq+q
2
)
=5(b−a)(c−b)(c−a)((p+q)
2
−pq)
=5(a−b)(b−c)(c−a)((c−a)
2
−bc−ab+ac+b
2
)=5(a−b)(b−c)(c−a)(a
2
+b
2
+c
2
−ab−bc−ca)
Hence, (a−b)
5
+(b−c)
5
+(c−a)
5
=5(a−b)(b−c)(c−a)(a
2
+b
2
+c
2
−ab−bc−ca).
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4
it can be factories as ........................ bro.
Step-by-step explanation:
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