Factorise : a^2-b^2+2bc-c^2
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a^2-b^2+2bc-c^2
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=(a+b-c)[a-(b-c)]
=(a+b-c)(a-b+c)
=a^2-(b^2-2bc+c^2)
=a^2-(b-c)^2
=(a+b-c)[a-(b-c)]
=(a+b-c)(a-b+c)
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2
Solution ●●●●
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![= {a}^{2} - ( {b}^{2} - 2.b.c + {c}^{2} ) \\ \\ = ({a})^{2} - ( {b - c})^{2} \\ \\ = (a + b - c)[a - (b - c)] \\ \\ = (a + b - c)(a - b + c)](https://tex.z-dn.net/?f=+%3D+%7Ba%7D%5E%7B2%7D+-+%28+%7Bb%7D%5E%7B2%7D+-+2.b.c+%2B+%7Bc%7D%5E%7B2%7D+%29+%5C%5C+%5C%5C+%3D+%28%7Ba%7D%29%5E%7B2%7D+-+%28+%7Bb+-+c%7D%29%5E%7B2%7D+%5C%5C+%5C%5C+%3D+%28a+%2B+b+-+c%29%5Ba+-+%28b+-+c%29%5D+%5C%5C+%5C%5C+%3D+%28a+%2B+b+-+c%29%28a+-+b+%2B+c%29 "= {a}^{2} - ( {b}^{2} - 2.b.c + {c}^{2} ) \\ \\ = ({a})^{2} - ( {b - c})^{2} \\ \\ = (a + b - c)[a - (b - c)] \\ \\ = (a + b - c)(a - b + c)")
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