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先化简,再求值:
(1) $a - \{ b - 2a + [3a - 2(2a + b) + 5b] \}$,其中$a, b$满足$a - b = 7$;
(2) $4x^2 - \frac{1}{3}xy - [ y^2 + \frac{1}{4}(28x^2 - \frac{4}{3}xy + 8y^2) ]$,其中$x, y$满足$x^2 + y^2 = 4$;
(3) $\frac{1}{3}mn - ( \frac{1}{3}n^2 - \frac{2}{3}mn ) + 2[ ( \frac{3}{2}mn - \frac{1}{3}n^2 ) +5 ]$,其中$m, n$满足$|m - 3| + (n + 2)^2 = 0$;
(4) $3a^2b - [ 2ab^2 - 2(2ab - \frac{5}{2}a^2b) + 2ab ] + 3(ab^2 - ab)$,其中$a, b$满足$(a + 4)^{2022} + \left| b - \frac{1}{2} \right| = 0$.
(1) $a - \{ b - 2a + [3a - 2(2a + b) + 5b] \}$,其中$a, b$满足$a - b = 7$;
(2) $4x^2 - \frac{1}{3}xy - [ y^2 + \frac{1}{4}(28x^2 - \frac{4}{3}xy + 8y^2) ]$,其中$x, y$满足$x^2 + y^2 = 4$;
(3) $\frac{1}{3}mn - ( \frac{1}{3}n^2 - \frac{2}{3}mn ) + 2[ ( \frac{3}{2}mn - \frac{1}{3}n^2 ) +5 ]$,其中$m, n$满足$|m - 3| + (n + 2)^2 = 0$;
(4) $3a^2b - [ 2ab^2 - 2(2ab - \frac{5}{2}a^2b) + 2ab ] + 3(ab^2 - ab)$,其中$a, b$满足$(a + 4)^{2022} + \left| b - \frac{1}{2} \right| = 0$.
答案
(1) 化简结果为$4a-4b$，值为28
(2) 化简结果为$-3x^2-3y^2$，值为-12
(3) 化简结果为$4mn-n^2+10$，值为-18
(4) 化简结果为$-2a^2b+ab^2-ab$，值为-15
【解析】原式 $=-2a^2b+ab^2-ab$.
$\because (a+4)^{2022}+\left| b-\frac{1}{2} \right| =0,\therefore a=-4$,
$b=\frac{1}{2}, \therefore$ 原式 $=-2×(-4)^2×\frac{1}{2}+(-4)×(\frac{1}{2})^2-(-4)×\frac{1}{2}=-15$.
(2) 化简结果为$-3x^2-3y^2$，值为-12
(3) 化简结果为$4mn-n^2+10$，值为-18
(4) 化简结果为$-2a^2b+ab^2-ab$，值为-15
【解析】原式 $=-2a^2b+ab^2-ab$.
$\because (a+4)^{2022}+\left| b-\frac{1}{2} \right| =0,\therefore a=-4$,
$b=\frac{1}{2}, \therefore$ 原式 $=-2×(-4)^2×\frac{1}{2}+(-4)×(\frac{1}{2})^2-(-4)×\frac{1}{2}=-15$.
