Toán Lớp 8: Rút gọn :
(a+b+c)^3 +(a-b-c)^3
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Toán Lớp 8: Rút gọn :
(a+b+c)^3 +(a-b-c)^3
Comments ( 2 )
{\left( {a + b + c} \right)^3} – {\left( {a – b – c} \right)^3}\\
= {\left[ {a + \left( {b + c} \right)} \right]^3} + {\left[ {a – \left( {b + c} \right)} \right]^3}\\
= {a^3} + {\left( {b + c} \right)^3} + 3a\left( {b + c} \right)\left( {a + b + c} \right) + \left[ {{a^3} – 3a\left( {b + c} \right)\left( {a – b – c} \right) – {{\left( {b + c} \right)}^3}} \right]\\
= 2{a^3} + 6a{\left( {b + c} \right)^2}\\
= 2{a^3} + 6a\left( {{b^2} + 2bc + {c^2}} \right)\\
= 2{a^3} + 6a{b^2} + 12abc + 6a{c^2}
\end{array}$