Toán Lớp 8: c,xy –2y – x^2+ 4
d) (x +2) (x + 3) (x + 4) (x + 5) – 24
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Toán Lớp 8: c,xy –2y – x^2+ 4
d) (x +2) (x + 3) (x + 4) (x + 5) – 24
Comments ( 1 )
c)xy – 2y – {x^2} + 4\\
= y\left( {x – 2} \right) – \left( {{x^2} – 4} \right)\\
= y\left( {x – 2} \right) – \left( {x – 2} \right)\left( {x + 2} \right)\\
= \left( {x – 2} \right)\left( {y – x – 2} \right)\\
d)\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\\
Dat:\left( {{x^2} + 7x + 10} \right) = 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}$