Toán Lớp 8: PTDTTNT
1/ 5x^2z – 15xyz + 30 xz^2
2/ a^3 – 3a + 3b – b^3
3/ 25 – a^2 – 2ab – b^2
4/ 4x^2 – 25 + (2x+7)(5-2x)
5/ a^2x^2 – a^2y^2 – b^2x^2 + b^2y^2
6/ x^2 – y^2 + 12y-36
7/ (x + 2)^2 – x^2 + 2x – 1
8/ 16x^2 – y^2
9/ 1 + 27x^3
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1)\\
5{x^2}z – 15xyz + 30x{z^2}\\
= 5xz\left( {x – 3y + 6z} \right)\\
2){a^3} – 3a + 3b – {b^3}\\
= {a^3} – {b^3} – 3\left( {a – b} \right)\\
= \left( {a – b} \right)\left( {{a^2} + ab + {b^2}} \right) – 3\left( {a – b} \right)\\
= \left( {a – b} \right)\left( {{a^2} + ab + {b^2} – 3} \right)\\
3)25 – {a^2} – 2ab – {b^2}\\
= 25 – {\left( {a + b} \right)^2}\\
= \left( {5 – a – b} \right)\left( {5 + a + b} \right)\\
4)\\
4{x^2} – 25 + \left( {2x + 7} \right)\left( {5 – 2x} \right)\\
= \left( {2x – 5} \right)\left( {2x + 5} \right) – \left( {2x – 5} \right)\left( {2x + 7} \right)\\
= \left( {2x – 5} \right)\left( {2x + 5 – 2x – 7} \right)\\
= \left( {2x – 5} \right).\left( { – 2} \right)\\
5)\\
{a^2}{x^2} – {a^2}{y^2} – {b^2}{x^2} + {b^2}{y^2}\\
= {a^2}\left( {{x^2} – {y^2}} \right) – {b^2}\left( {{x^2} – {y^2}} \right)\\
= \left( {{x^2} – {y^2}} \right)\left( {{a^2} – {b^2}} \right)\\
= \left( {x – y} \right)\left( {x + y} \right)\left( {a – b} \right)\left( {a + b} \right)\\
6){x^2} – {y^2} + 12y – 36\\
= {x^2} – {\left( {y – 6} \right)^2}\\
= \left( {x – y + 6} \right)\left( {x + y – 6} \right)\\
7){\left( {x + 2} \right)^2} – {x^2} + 2x – 1\\
= {\left( {x + 2} \right)^2} – {\left( {x – 1} \right)^2}\\
= \left( {x + 2 + x – 1} \right)\left( {x + 2 – x + 1} \right)\\
= \left( {2x + 1} \right).3\\
8)16{x^2} – {y^2}\\
= \left( {4x – y} \right)\left( {4x + y} \right)\\
9)1 + 27{x^3}\\
= \left( {1 + 3x} \right)\left( {1 – 3x + 9{x^2}} \right)
\end{array}$