a) 

\(\left(-12\right)+\left(-25\right)=-\left(12+25\right)=-37\\ 90+\left(-70\right)=90-70=20\\ \left(-234+11\right)=-\left(234-11\right)=-223\\ \left(-54\right)+\left(-9\right)+90=90-54-9=27\)

b)

\(\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4\\ =\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+4\\ =0+0+0+4\\ =4\)

a) 

\(126+\left(-10\right)+\left(-100\right)+\left(-126\right)=\left[126+\left(-126\right)\right]-\left(10+100\right)\\ =0-110\\ =-110\)

b) 

\(\left(-213\right)+89+13+11\\ =\left[-213+13\right]+\left(89+11\right)\\ =-200+100\\ =-100\)

\(\dfrac{x}{17}+\dfrac{19}{34}=2\dfrac{1}{2}\\ \dfrac{x}{17}+\dfrac{19}{34}=\dfrac{5}{2}\\ \dfrac{x}{17}=\dfrac{5}{2}-\dfrac{19}{34}\\ \dfrac{x}{17}=\dfrac{33}{17}\\ x=33\)

\(\left(x+3\right)\left(x^2+3x-5\right)\\ =x^3+3x^2-5x+3x^2+9x-15\\ =x^3+6x^2+4x-15\)

a) 

\(\left(-12\right)+\left(-25\right)=-\left(12+25\right)=-37\\ 90+\left(-70\right)=90-70=20\\ \left(-234+11\right)=-\left(234-11\right)=-223\\ \left(-54\right)+\left(-9\right)+90=90-54-9=27\)

b)

\(\left(-3\right)+\left(-2\right)+\left(-1\right)+0+1+2+3+4\\ =\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+4\\ =0+0+0+4\\ =4\)

\(\dfrac{84}{x}=\dfrac{12}{23}\Rightarrow x=\dfrac{84\times23}{12}=161\)