a) \(2x\left(2x+1\right)-\left(2x+3\right)\left(2x-3\right)=1\)
\(\Rightarrow4x^2+2x-\left(4x^2-9\right)=1\)
\(\Rightarrow2x+9=1\Rightarrow2x=-8\Leftrightarrow x=-4\)
b) \(\left(x+4\right)^2-\left(x+1\right)\left(x-1\right)=16\)
\(\Rightarrow x^2+8x+16-(x^2-1)=16\)
\(\Rightarrow8x+16+1=16\Rightarrow8x=-1\) \(\Rightarrow x=-\dfrac{1}{8}\)
c) \(\left(y-2\right)^3-\left(y-3\right)\left(y^2+3y+9\right)+6\left(y+1\right)^2=49\)
\(\Rightarrow y^3-6y^2+12y-8-\left(y^3-3^3\right)+6\left(y^2+2y+1\right)=49\)
\(\Rightarrow12y-8+27+12y+6=49\)
\(\Rightarrow24y=24\Rightarrow y=1\)
d) \(\left(y+3\right)^3-\left(y+1\right)^3=56\)
\(\Rightarrow y^3+9y^2+27y+27-\left(y^3+3y^2+3y+1\right)=56\)
\(\Rightarrow6y^2+24y+26=56\Rightarrow6y^2+24y-30=0\)
\(\Rightarrow\left[{}\begin{matrix}y=1\\y=-5\end{matrix}\right.\)
