\(\left(3x-1\right)^2-4^2=\left(3x-1-4\right)\left(3x-1+4\right)=\left(3x-5\right)\left(3x+3\right)=3\left(x+1\right)\left(3x-5\right)\)
\(\left(5x-4\right)^2-\left(7x\right)^2=\left(5x-4-7x\right)\left(5x-5+7x\right)=-2\left(x+2\right)\left(12x-5\right)\)
\(\left(3x+1\right)^2-\left(2x-4\right)^2=\left(3x+1-2x+4\right)\left(3x+1+2x-4\right)=\left(x+5\right)\left(5x-3\right)\)
\(\left(6x+9\right)^2-\left(2x+2\right)^2=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)=\left(4x+7\right)\left(8x+11\right)\)
\(\left(2bc\right)^2-\left(b^2+c^2-a^2\right)^2=\left(2bc+b^2+c^2-a^2\right)\left(2bc-b^2-c^2+a^2\right)\)
\(=\left[\left(b+c\right)^2-a^2\right]\left[a^2-\left(b-c\right)^2\right]\)
\(=\left(b+c-a\right)\left(b+c+a\right)\left(a-b+c\right)\left(a+b-c\right)\)