2. 计算:
(1) $24a - 25a$;
(2) $7x^2y - 3x^2y$;
(3) $0.25a^2b - \frac{3}{4}a^2b$;
(4) $\frac{1}{3}m^3n^2 - 3m^3n^2$;
(5) $10xy - \frac{7}{2}xy - 3xy$;
(6) $-a^2b + 3ab^2 + 2a^2b - \frac{1}{3}ab^2$。
(1) $24a - 25a$;
(2) $7x^2y - 3x^2y$;
(3) $0.25a^2b - \frac{3}{4}a^2b$;
(4) $\frac{1}{3}m^3n^2 - 3m^3n^2$;
(5) $10xy - \frac{7}{2}xy - 3xy$;
(6) $-a^2b + 3ab^2 + 2a^2b - \frac{1}{3}ab^2$。
答案
2. (1)$-a$ (2)$4x^2y$ (3)$-\frac{1}{2}a^2b$
(4)$-\frac{8}{3}m^3n^2$ (5)$\frac{7}{2}xy$ (6)$a^2b+\frac{8}{3}ab^2$
(4)$-\frac{8}{3}m^3n^2$ (5)$\frac{7}{2}xy$ (6)$a^2b+\frac{8}{3}ab^2$
3. 若多项式$a^2 + kab$与$b^2 - 3ab$的和不含有ab项,求$k^2$的值.
答案
3. 9
阅读材料:“整体思想”是中学数学的重要思想方法,在解题中会经常用到.我们知道,合并同类项:$4x - 2x + x = (4 - 2 + 1)x = 3x$,类似地,我们把$(a + b)$看成一个整体,则$4(a + b) - 2(a + b) + (a + b) = (4 - 2 + 1)(a + b) = 3(a + b)$.
尝试应用:
(1)把$(a - b)^2$看成一个整体,合并$3(a - b)^2 - 6(a - b)^2 + 2(a - b)^2$的结果是
(2)已知$x^2 - 2y = 4$,求$3x^2 - 6y - 21$的值.
拓展探索:
(3)已知$a - 2b = 3$,$2b - c = -5$,求$a - c$的值.
尝试应用:
(1)把$(a - b)^2$看成一个整体,合并$3(a - b)^2 - 6(a - b)^2 + 2(a - b)^2$的结果是
$-(a-b)^2$
.(2)已知$x^2 - 2y = 4$,求$3x^2 - 6y - 21$的值.
拓展探索:
(3)已知$a - 2b = 3$,$2b - c = -5$,求$a - c$的值.
答案
(1)$-(a-b)^2$ (2)$-9$ (3)$-2$
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