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17. (本题9分)定义一种新运算,观察下列式子:
$1☆4 = 1×3 + 4×2 = 11$;
$3☆(-1) = 3×3 + (-1)×2 = 7$;
$5☆4 = 5×3 + 4×2 = 23$;
$4☆(-2) = 4×3 + (-2)×2 = 8$;
若$a、b$符合上面式子的规律.
(1) $a☆b=$
(2) 已知$a☆b = 2$,求$(a - 2b)☆(3a + 6b)$的值.
$1☆4 = 1×3 + 4×2 = 11$;
$3☆(-1) = 3×3 + (-1)×2 = 7$;
$5☆4 = 5×3 + 4×2 = 23$;
$4☆(-2) = 4×3 + (-2)×2 = 8$;
若$a、b$符合上面式子的规律.
(1) $a☆b=$
3a + 2b
(用含$a、b$的代数式表示);(2) 已知$a☆b = 2$,求$(a - 2b)☆(3a + 6b)$的值.
答案：
17.
(1)$3a + 2b$
(2)6
(1)$3a + 2b$
(2)6
18. (本题9分)已知$x^{2}-xy = 4,y^{2}-xy = 9$,求下列各代数式的值:
(1)$x^{2}-2xy + y^{2}$;
(2)$x^{2}-y^{2}$;
(3)$2x^{2}+xy - 3y^{2}$.
(1)$x^{2}-2xy + y^{2}$;
(2)$x^{2}-y^{2}$;
(3)$2x^{2}+xy - 3y^{2}$.
答案：
18.
(1)$x^{2}-2xy + y^{2}=x^{2}-xy + y^{2}-xy = 4 + 9 = 13$
(2)$x^{2}-y^{2}=x^{2}-xy-(y^{2}-xy)=4 - 9 = -5$
(3)$2x^{2}+xy-3y^{2}=2(x^{2}-y^{2})-(y^{2}-xy)=-10 - 9 = -19$
(1)$x^{2}-2xy + y^{2}=x^{2}-xy + y^{2}-xy = 4 + 9 = 13$
(2)$x^{2}-y^{2}=x^{2}-xy-(y^{2}-xy)=4 - 9 = -5$
(3)$2x^{2}+xy-3y^{2}=2(x^{2}-y^{2})-(y^{2}-xy)=-10 - 9 = -19$
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