a ^ 2 - (b ^ 2 - 2bc + c ^ 2)
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Answer:
Given : a
2
−b
2
+2bc−c
2
We can write it as
a
2
−b
2
+2bc−c
2
=a
2
−(b
2
−2bc+c
2
)
We know that, (a−b)
2
=a
2
−2ab−b
2
a
2
−b
2
+2bc−c
2
=a
2
−(b−c)
2
Based on the equation a
2
−b
2
=(a+b)(a−b)
We get,
a
2
−b
2
+2bc−c
2
=[a+(b−c)[a−(b−c)]
a
2
−b
2
+2bc−c
2
=(a+b−c)(a−b+c)
By taking (2a+3b) as common
a
2
−b
2
+2bc−c
2
=(2a+3b)(2a−3b−1)
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