Toán Lớp 8: a^2(b-c)+c^2(a-b)+b^2(c-a)=-(b-a)*(c-a)*(c-b)
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Toán Lớp 8: a^2(b-c)+c^2(a-b)+b^2(c-a)=-(b-a)*(c-a)*(c-b)
Comments ( 1 )
{a^2}\left( {b – c} \right) + {c^2}\left( {a – b} \right) + {b^2}\left( {c – a} \right)\\
= {a^2}b – {a^2}c + a{c^2} – b{c^2} + {b^2}\left( {c – a} \right)\\
= {a^2}b – b{c^2} – {a^2}c + a{c^2} + {b^2}\left( {c – a} \right)\\
= b\left( {{a^2} – {c^2}} \right) – ac\left( {a – c} \right) – {b^2}\left( {a – c} \right)\\
= b\left( {a + c} \right)\left( {a – c} \right) – ac\left( {a – c} \right) – {b^2}\left( {a – c} \right)\\
= \left( {a – c} \right)\left( {ab + bc – ac – {b^2}} \right)\\
= \left( {a – c} \right).\left( {ab – {b^2} + bc – ac} \right)\\
= \left( {a – c} \right).\left( {a – b} \right)\left( {b – c} \right)\\
= \left( {b – a} \right).\left( {c – a} \right).\left( {c – b} \right)
\end{array}$