(1)$(-2ab+3b)-2(-b)-2ab$; (2)$5(ab-3ab^{2})-2(a^{2}b-7ab)$;
(3)$3(2x^{2}y-xy^{2})-(4xy^{2}+3x^{2}y)$; (4)$-3(2x^{2}-xy)+4(x^{2}+xy-6)$;
(5)$2a^{2}+9b^{2}+(-5a^{2}-4b^{2})$; (6)$a+[2a-2-(4-2a)]$;
(7)$3x^{2}-[7x-(4x-3)-2x^{2}]$; (8)$-(3a^{2}-4ab)+[a^{2}-2(2a+2ab)]$;
(9)$2a^{2}b+2ab^{2}-[2(a^{2}b-1)+2ab^{2}+2]$; (10)$1-3(2ab+a)+[1-2(2a-3ab)]$.
(3)$3(2x^{2}y-xy^{2})-(4xy^{2}+3x^{2}y)$; (4)$-3(2x^{2}-xy)+4(x^{2}+xy-6)$;
(5)$2a^{2}+9b^{2}+(-5a^{2}-4b^{2})$; (6)$a+[2a-2-(4-2a)]$;
(7)$3x^{2}-[7x-(4x-3)-2x^{2}]$; (8)$-(3a^{2}-4ab)+[a^{2}-2(2a+2ab)]$;
(9)$2a^{2}b+2ab^{2}-[2(a^{2}b-1)+2ab^{2}+2]$; (10)$1-3(2ab+a)+[1-2(2a-3ab)]$.
答案:(1)-4ab+5b (2)19ab-15ab²-2a²b (3)3x²y-7xy² (4)-2x²+7xy-24 (5)-3a²+5b² (6)5a-6 (7)5x²-3x-3 (8)-2a²-4a (9)0 (10)2-7a
解析:
(1)
$\begin{aligned}(-2ab + 3b) - 2(-b) - 2ab&=-2ab + 3b + 2b - 2ab\\&=(-2ab - 2ab) + (3b + 2b)\\&=-4ab + 5b\end{aligned}$
(2)
$\begin{aligned}5(ab - 3ab^2) - 2(a^2b - 7ab)&=5ab - 15ab^2 - 2a^2b + 14ab\\&=(5ab + 14ab) - 15ab^2 - 2a^2b\\&=19ab - 15ab^2 - 2a^2b\end{aligned}$
(3)
$\begin{aligned}3(2x^2y - xy^2) - (4xy^2 + 3x^2y)&=6x^2y - 3xy^2 - 4xy^2 - 3x^2y\\&=(6x^2y - 3x^2y) + (-3xy^2 - 4xy^2)\\&=3x^2y - 7xy^2\end{aligned}$
(4)
$\begin{aligned}-3(2x^2 - xy) + 4(x^2 + xy - 6)&=-6x^2 + 3xy + 4x^2 + 4xy - 24\\&=(-6x^2 + 4x^2) + (3xy + 4xy) - 24\\&=-2x^2 + 7xy - 24\end{aligned}$
(5)
$\begin{aligned}2a^2 + 9b^2 + (-5a^2 - 4b^2)&=2a^2 + 9b^2 - 5a^2 - 4b^2\\&=(2a^2 - 5a^2) + (9b^2 - 4b^2)\\&=-3a^2 + 5b^2\end{aligned}$
(6)
$\begin{aligned}a + [2a - 2 - (4 - 2a)]&=a + [2a - 2 - 4 + 2a]\\&=a + (4a - 6)\\&=a + 4a - 6\\&=5a - 6\end{aligned}$
(7)
$\begin{aligned}3x^2 - [7x - (4x - 3) - 2x^2]&=3x^2 - [7x - 4x + 3 - 2x^2]\\&=3x^2 - (3x + 3 - 2x^2)\\&=3x^2 - 3x - 3 + 2x^2\\&=(3x^2 + 2x^2) - 3x - 3\\&=5x^2 - 3x - 3\end{aligned}$
(8)
$\begin{aligned}-(3a^2 - 4ab) + [a^2 - 2(2a + 2ab)]&=-3a^2 + 4ab + [a^2 - 4a - 4ab]\\&=-3a^2 + 4ab + a^2 - 4a - 4ab\\&=(-3a^2 + a^2) + (4ab - 4ab) - 4a\\&=-2a^2 - 4a\end{aligned}$
(9)
$\begin{aligned}2a^2b + 2ab^2 - [2(a^2b - 1) + 2ab^2 + 2]&=2a^2b + 2ab^2 - [2a^2b - 2 + 2ab^2 + 2]\\&=2a^2b + 2ab^2 - (2a^2b + 2ab^2)\\&=2a^2b + 2ab^2 - 2a^2b - 2ab^2\\&=0\end{aligned}$
(10)
$\begin{aligned}1 - 3(2ab + a) + [1 - 2(2a - 3ab)]&=1 - 6ab - 3a + [1 - 4a + 6ab]\\&=1 - 6ab - 3a + 1 - 4a + 6ab\\&=(1 + 1) + (-6ab + 6ab) + (-3a - 4a)\\&=2 - 7a\end{aligned}$
$\begin{aligned}(-2ab + 3b) - 2(-b) - 2ab&=-2ab + 3b + 2b - 2ab\\&=(-2ab - 2ab) + (3b + 2b)\\&=-4ab + 5b\end{aligned}$
(2)
$\begin{aligned}5(ab - 3ab^2) - 2(a^2b - 7ab)&=5ab - 15ab^2 - 2a^2b + 14ab\\&=(5ab + 14ab) - 15ab^2 - 2a^2b\\&=19ab - 15ab^2 - 2a^2b\end{aligned}$
(3)
$\begin{aligned}3(2x^2y - xy^2) - (4xy^2 + 3x^2y)&=6x^2y - 3xy^2 - 4xy^2 - 3x^2y\\&=(6x^2y - 3x^2y) + (-3xy^2 - 4xy^2)\\&=3x^2y - 7xy^2\end{aligned}$
(4)
$\begin{aligned}-3(2x^2 - xy) + 4(x^2 + xy - 6)&=-6x^2 + 3xy + 4x^2 + 4xy - 24\\&=(-6x^2 + 4x^2) + (3xy + 4xy) - 24\\&=-2x^2 + 7xy - 24\end{aligned}$
(5)
$\begin{aligned}2a^2 + 9b^2 + (-5a^2 - 4b^2)&=2a^2 + 9b^2 - 5a^2 - 4b^2\\&=(2a^2 - 5a^2) + (9b^2 - 4b^2)\\&=-3a^2 + 5b^2\end{aligned}$
(6)
$\begin{aligned}a + [2a - 2 - (4 - 2a)]&=a + [2a - 2 - 4 + 2a]\\&=a + (4a - 6)\\&=a + 4a - 6\\&=5a - 6\end{aligned}$
(7)
$\begin{aligned}3x^2 - [7x - (4x - 3) - 2x^2]&=3x^2 - [7x - 4x + 3 - 2x^2]\\&=3x^2 - (3x + 3 - 2x^2)\\&=3x^2 - 3x - 3 + 2x^2\\&=(3x^2 + 2x^2) - 3x - 3\\&=5x^2 - 3x - 3\end{aligned}$
(8)
$\begin{aligned}-(3a^2 - 4ab) + [a^2 - 2(2a + 2ab)]&=-3a^2 + 4ab + [a^2 - 4a - 4ab]\\&=-3a^2 + 4ab + a^2 - 4a - 4ab\\&=(-3a^2 + a^2) + (4ab - 4ab) - 4a\\&=-2a^2 - 4a\end{aligned}$
(9)
$\begin{aligned}2a^2b + 2ab^2 - [2(a^2b - 1) + 2ab^2 + 2]&=2a^2b + 2ab^2 - [2a^2b - 2 + 2ab^2 + 2]\\&=2a^2b + 2ab^2 - (2a^2b + 2ab^2)\\&=2a^2b + 2ab^2 - 2a^2b - 2ab^2\\&=0\end{aligned}$
(10)
$\begin{aligned}1 - 3(2ab + a) + [1 - 2(2a - 3ab)]&=1 - 6ab - 3a + [1 - 4a + 6ab]\\&=1 - 6ab - 3a + 1 - 4a + 6ab\\&=(1 + 1) + (-6ab + 6ab) + (-3a - 4a)\\&=2 - 7a\end{aligned}$