Toán Lớp 8: A) (a-b-c)^2 – (a-b+c)^2
B) (a-x-y)^3 – (a+x-y)^3
C) (1+x+x^2).(1-x).(1+x).(1-x+x^2)
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Toán Lớp 8: A) (a-b-c)^2 – (a-b+c)^2
B) (a-x-y)^3 – (a+x-y)^3
C) (1+x+x^2).(1-x).(1+x).(1-x+x^2)
Comments ( 1 )
a){\left( {a – b – c} \right)^2} – {\left( {a – b + c} \right)^2}\\
= \left( {a – b – c + a – b + c} \right)\left( {a – b – c – a + b – c} \right)\\
= \left( {2a – 2b} \right).\left( { – 2c} \right)\\
= – 4ac + 4bc\\
b){\left( {a – x – y} \right)^3} – {\left( {a + x – y} \right)^3}\\
= {\left( {a – y – x} \right)^3} – {\left( {a – y + x} \right)^3}\\
= {\left( {a – y} \right)^3} – 3{\left( {a – y} \right)^2}.x + 3\left( {a – y} \right){x^2} – {x^3}\\
– \left( {{{\left( {a – y} \right)}^3} + 3{{\left( {a – y} \right)}^2}x + 3\left( {a – y} \right){x^2} + {x^3}} \right)\\
= – 6{\left( {a – y} \right)^2}x – 2{x^3}\\
= – 6{a^2}x + 12ayx – 6{y^2}x – 2{x^3}\\
c)\left( {1 + x + {x^2}} \right)\left( {1 – x} \right)\left( {1 + x} \right)\left( {1 – x + {x^2}} \right)\\
= \left( {1 – {x^3}} \right)\left( {1 + {x^3}} \right)\\
= 1 – {x^6}
\end{array}$