\(x^2+8xy+16y^2+2x+8y-3\)
\(=x^2+2.x.4y+\left(4y\right)^2+2\left(x+4y\right)-3\)
\(=\left(x+4y\right)^2+2\left(x+4y\right)+1-2^2\)
\(=\left(x+4y+1\right)^2-2^2\)
\(=\left(x+4y+1-2\right)\left(x+4y+1+2\right)\)
\(=\left(x+4y-1\right)\left(x+4y+3\right)\)
\(4x^2+4xy+y^2+10x+5y-6\)
\(=\left(2x\right)^2+2.2x.y+y^2+5\left(2x+y\right)-6\)
\(=\left(2x+y\right)^2+5\left(2x+y\right)-6\)
\(=\left(2x+y\right)^2+2\left(2x+y\right).\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2-\left(\dfrac{7}{2}\right)^2\)
\(=\left(2x+y+\dfrac{5}{2}\right)^2-\left(\dfrac{7}{2}\right)^2\)
\(=\left(2x+y+\dfrac{5}{2}-\dfrac{7}{2}\right)\left(2x+y+\dfrac{5}{2}+\dfrac{7}{2}\right)\)
\(=\left(2x+y-1\right)\left(2x+y+6\right)\)
