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信息發(fā)布者：
$12$
$23$
解：
$\begin{aligned}&(2x - y)^2 - (x - y)(x + y)\\=&4x^2-4xy + y^2-(x^2 - y^2)\\=&4x^2-4xy + y^2 - x^2 + y^2\\=&3x^2-4xy + 2y^2\end{aligned}$
解：
$\begin{aligned}&(3x + y)^2(3x - y)^2\\=&[(3x + y)(3x - y)]^2\\=&(9x^2 - y^2)^2\\=&81x^4-18x^2y^2 + y^4\end{aligned}$
解：
$\begin{aligned}&(x + 2y + 3z)(x + 2y - 3z)\\=&[(x + 2y)+3z][(x + 2y)-3z]\\=&(x + 2y)^2-9z^2\\=&x^2 + 4xy+4y^2-9z^2\end{aligned}$
解：
?$ \begin {aligned}&(2y + 3x)(3x - 2y)-4y(x - y)\\=&9x^2-4y^2-4xy + 4y^2\\=&9x^2-4xy\end {aligned}$?
?$ $?當(dāng)?$x = \frac {1}{3}，$??$y=-2$?時(shí)，
?$ \begin {aligned}&9×(\frac {1}{3})^2-4×\frac {1}{3}×(-2)\\=&9×\frac {1}{9}+\frac {8}{3}\\=&1+\frac {8}{3}\\=&\frac {11}{3}\end {aligned}$?
解：
?$ \begin {aligned}&(x - 3)^2+2(x - 2)(x + 7)-(x + 2)(x - 2)\\=&x^2-6x + 9+2(x^2+7x-2x-14)-(x^2 - 4)\\=&x^2-6x + 9+2x^2+14x-4x-28-x^2 + 4\\=&2x^2+4x-15\end {aligned}$?
?$ $?因?yàn)?$x^2+2x - 4 = 0，$?
所以?$x^2+2x = 4。$?
?$ $?當(dāng)?$x^2+2x = 4$?時(shí)，
?$ \begin {aligned}&2(x^2+2x)-15\\=&2×4-15\\=&8 - 15\\=&-7\end {aligned}$?
解：?$ (1)$?由題意得，?$S_{1}=(2m + 4)(m + 2)$?
?$=2\ \mathrm {m^2}+4m+4m + 8=2\ \mathrm {m^2}+8m + 8；$?
?$ S_{2}=\frac {1}{2}(2m + 4)(m - 2)$?
?$=\frac {1}{2}(2\ \mathrm {m^2}-4)=\mathrm {m^2}-4。$?
?$ (2)$?是定值。
 由題意得，?$S_{3}=(3m + 4)^2=9\ \mathrm {m^2}+24m + 16，$?
?$ \begin {aligned}&S_{3}-3(S_{1}+S_{2})\\=&9\ \mathrm {m^2}+24m + 16-3(2\ \mathrm {m^2}+8m + 8+\mathrm {m^2}-4)\\=&9\ \mathrm {m^2}+24m + 16-3(3\ \mathrm {m^2}+8m + 4)\\=&9\ \mathrm {m^2}+24m + 16-9\ \mathrm {m^2}-24m-12\\=&4\end {aligned}$?
$9^2-7^2 = 8\times4$
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