Đáp án:

$\begin{array}{l}
a)25.\left( {75 - 49} \right) + 75\left| {25 - 49} \right|\\
 = 25.75 - 25.49 + 75.\left( {49 - 25} \right)\\
 = 25.75 - 25.49 + 75.49 - 75.25\\
 = 49.\left( {75 - 25} \right)\\
 = 49.50\\
 = 2450\\
b)23.\left( {64 - 51} \right) - 51.\left( { - 23 - 64} \right) - 26.\left( { - 64} \right)\\
 = 23.64 - 23.51 + 51.23 + 51.64 + 26.64\\
 = \left( {23.64 + 26.64} \right) + 51.\left( { - 23 + 23 + 64} \right)\\
 = 64.\left( {23 + 26 + 51} \right)\\
 = 64.100\\
 = 6400\\
2)a) - 7 - 2x =  - 1\\
 \Rightarrow 2x =  - 6\\
 \Rightarrow x =  - 3\\
Vậy\,x =  - 3\\
b)125 - 3.\left( {x + 18} \right) = 77\\
 \Rightarrow 3\left( {x + 18} \right) = 125 - 77\\
 \Rightarrow 3.\left( {x + 18} \right) = 48\\
 \Rightarrow x + 18 = 16\\
 \Rightarrow x =  - 2\\
Vậy\,x =  - 2\\
c)\left( {x + 3} \right)\left( {2 - x} \right) = 0\\
 \Rightarrow \left[ \begin{array}{l}
x =  - 3\\
x = 2
\end{array} \right.\\
Vậy\,x =  - 3;x = 2\\
d)\left( { - 100} \right):{\left( {2x - 7} \right)^2} =  - 4\\
 \Rightarrow {\left( {2x - 7} \right)^2} = 25\\
 \Rightarrow \left[ \begin{array}{l}
2x - 7 = 5\\
2x - 7 =  - 5
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
2x = 12\\
2x = 2
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x = 6\\
x = 1
\end{array} \right.\\
Vậy\,x = 6;x = 1\\
e){\left( {1 - 3x} \right)^3} =  - 8\\
 \Rightarrow 1 - 3x =  - 2\\
 \Rightarrow 3x = 3\\
 \Rightarrow x = 1\\
Vậy\,x = 1\\
f) - 9 - \left( {21 - 3x} \right) =  - 215 - \left( {84 - 215} \right)\\
 \Rightarrow  - 9 - 21 + 3x =  - 215 - 84 + 215\\
 \Rightarrow 3x - 30 =  - 84\\
 \Rightarrow 3x =  - 54\\
 \Rightarrow x =  - 18\\
Vậy\,x =  - 18\\
g)5\left( {3 - x} \right) - 2\left( {7 - x} \right) =  - 14\\
 \Rightarrow 15 - 5x - 14 + 2x =  - 14\\
 \Rightarrow 3x = 15\\
 \Rightarrow x = 5\\
Vậy\,x = 5\\
h)3\left| {3x - 1} \right| + 5 = 14\\
 \Rightarrow \left| {3x - 1} \right| = 3\\
 \Rightarrow \left[ \begin{array}{l}
3x - 1 = 3\\
3x - 1 =  - 3
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x = \frac{4}{3}\\
x = \frac{2}{3}
\end{array} \right.\\
i)\left( {x + 2} \right)\left( {x - 3} \right) < 0\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x + 2 > 0\\
x - 3 < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x + 2 < 0\\
x - 3 > 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x >  - 2\\
x < 3
\end{array} \right.\\
\left\{ \begin{array}{l}
x <  - 2\\
x > 3
\end{array} \right.\left( {ktm} \right)
\end{array} \right.\\
Vậy\, - 2 < x < 3
\end{array}$

$\begin{array}{l}
k)\left( {{x^2} + 1} \right)\left( {25 - {x^2}} \right) = 0\\
 \Rightarrow 25 - {x^2} = 0\left( {do:{x^2} + 1 > 0} \right)\\
 \Rightarrow {x^2} = 25\\
 \Rightarrow x =  \pm 5
\end{array}$

$\begin{array}{l} a)25.\left( {75 - 49} \right) + 75\left| {25 - 49} \right|\\  = 25.75 - 25.49 + 75.\left( {49 - 25} \right)\\  = 25.75 - 25.49 + 75.49 - 75.25\\  = 49.\left( {75 - 25} \right)\\  = 49.50\\  = 2450\\ b)23.\left( {64 - 51} \right) - 51.\left( { - 23 - 64} \right) - 26.\left( { - 64} \right)\\  = 23.64 - 23.51 + 51.23 + 51.64 + 26.64\\  = \left( {23.64 + 26.64} \right) + 51.\left( { - 23 + 23 + 64} \right)\\  = 64.\left( {23 + 26 + 51} \right)\\  = 64.100\\  = 6400\\ 2)a) - 7 - 2x =  - 1\\  \Rightarrow 2x =  - 6\\  \Rightarrow x =  - 3\\ Vậy\,x =  - 3\\ b)125 - 3.\left( {x + 18} \right) = 77\\  \Rightarrow 3\left( {x + 18} \right) = 125 - 77\\  \Rightarrow 3.\left( {x + 18} \right) = 48\\  \Rightarrow x + 18 = 16\\  \Rightarrow x =  - 2\\ Vậy\,x =  - 2\\ c)\left( {x + 3} \right)\left( {2 - x} \right) = 0\\  \Rightarrow \left[ \begin{array}{l} x =  - 3\\ x = 2 \end{array} \right.\\ Vậy\,x =  - 3;x = 2\\ d)\left( { - 100} \right):{\left( {2x - 7} \right)^2} =  - 4\\  \Rightarrow {\left( {2x - 7} \right)^2} = 25\\  \Rightarrow \left[ \begin{array}{l} 2x - 7 = 5\\ 2x - 7 =  - 5 \end{array} \right.\\  \Rightarrow \left[ \begin{array}{l} 2x = 12\\ 2x = 2 \end{array} \right.\\  \Rightarrow \left[ \begin{array}{l} x = 6\\ x = 1 \end{array} \right.\\ Vậy\,x = 6;x = 1\\ e){\left( {1 - 3x} \right)^3} =  - 8\\  \Rightarrow 1 - 3x =  - 2\\  \Rightarrow 3x = 3\\  \Rightarrow x = 1\\ Vậy\,x = 1\\ f) - 9 - \left( {21 - 3x} \right) =  - 215 - \left( {84 - 215} \right)\\  \Rightarrow  - 9 - 21 + 3x =  - 215 - 84 + 215\\  \Rightarrow 3x - 30 =  - 84\\  \Rightarrow 3x =  - 54\\  \Rightarrow x =  - 18\\ Vậy\,x =  - 18\\ g)5\left( {3 - x} \right) - 2\left( {7 - x} \right) =  - 14\\  \Rightarrow 15 - 5x - 14 + 2x =  - 14\\  \Rightarrow 3x = 15\\  \Rightarrow x = 5\\ Vậy\,x = 5\\ h)3\left| {3x - 1} \right| + 5 = 14\\  \Rightarrow \left| {3x - 1} \right| = 3\\  \Rightarrow \left[ \begin{array}{l} 3x - 1 = 3\\ 3x - 1 =  - 3 \end{array} \right.\\  \Rightarrow \left[ \begin{array}{l} x = \frac{4}{3}\\ x = \frac{2}{3} \end{array} \right.\\ i)\left( {x + 2} \right)\left( {x - 3} \right) < 0\\  \Rightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} x + 2 > 0\\ x - 3 < 0 \end{array} \right.\\ \left\{ \begin{array}{l} x + 2 < 0\\ x - 3 > 0 \end{array} \right. \end{array} \right. \Rightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} x >  - 2\\ x < 3 \end{array} \right.\\ \left\{ \begin{array}{l} x <  - 2\\ x > 3 \end{array} \right.\left( {ktm} \right) \end{array} \right.\\ Vậy\, - 2 < x < 3 \end{array}$