Toán Lớp 8: Giúp mk với, mk cần gấp!!!
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1. x^3 + 27 – ( x + 3 ) × ( 3x + 4 )
2. ( 1 + 2x ) × ( 1 – 2x ) – ( x + 2 ) × ( x – 2 )
3. x^4 + 4
4. x^4 + x^2y^2 + y^2
5. (x + 2) × ( x + 3 ) × ( x + 4 ) × ( x + 5 ) – 24
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1){x^3} + 27 – \left( {x + 3} \right)\left( {3x + 4} \right)\\
= \left( {x + 3} \right)\left( {{x^2} – 3x + 9} \right) – \left( {x + 3} \right)\left( {3x + 4} \right)\\
= \left( {x + 3} \right)\left( {{x^2} – 3x + 9 – 3x – 4} \right)\\
= \left( {x + 3} \right)\left( {{x^2} – 6x + 5} \right)\\
= \left( {x + 3} \right)\left( {x – 1} \right)\left( {x – 5} \right)\\
2)\\
\left( {1 + 2x} \right)\left( {1 – 2x} \right) – \left( {x + 2} \right)\left( {x – 2} \right)\\
= {1^2} – {\left( {2x} \right)^2} – \left( {{x^2} – 4} \right)\\
= 1 – 4{x^2} – {x^2} + 4\\
= 5 – 5{x^2}\\
= 5.\left( {1 – {x^2}} \right)\\
= 5.\left( {1 – x} \right)\left( {1 + x} \right)\\
3){x^4} + 4\\
= {x^4} + 4{x^2} + 4 – 4{x^2}\\
= {\left( {{x^2} + 2} \right)^2} – 4{x^2}\\
= \left( {{x^2} + 2 + 2x} \right)\left( {{x^2} + 2 – 2x} \right)\\
4){x^4} + {x^2}{y^2} + {y^4}\\
= {x^4} + 2{x^2}{y^2} + {y^4} – {x^2}{y^2}\\
= {\left( {{x^2} + {y^2}} \right)^2} – {\left( {xy} \right)^2}\\
= \left( {{x^2} + {y^2} + xy} \right).\left( {{x^2} + {y^2} – xy} \right)\\
5)\left( {x + 2} \right)\left( {x + 3} \right)\left( {x + 4} \right)\left( {x + 5} \right) – 24\\
= \left( {x + 2} \right)\left( {x + 5} \right)\left( {x + 3} \right)\left( {x + 4} \right) – 24\\
= \left( {{x^2} + 7x + 10} \right)\left( {{x^2} + 7x + 12} \right) – 24\\
Đặt:{x^2} + 7x + 10 = a\\
\Leftrightarrow a.\left( {a + 2} \right) – 24\\
= {a^2} + 2a – 24\\
= {a^2} + 6a – 4a – 24\\
= \left( {a + 6} \right)\left( {a – 4} \right)\\
= \left( {{x^2} + 7x + 10 + 6} \right).\left( {{x^2} + 7x + 10 – 4} \right)\\
= \left( {{x^2} + 7x + 16} \right).\left( {{x^2} + 7x + 6} \right)\\
= \left( {{x^2} + 7x + 16} \right).\left( {x + 1} \right)\left( {x + 6} \right)
\end{array}$