\(27x^3+125y^3\)
\(=\left(3x\right)^3+\left(5y\right)^3\)
\(=\left(3x+5y\right)\left(9x^2-15xy+25y^2\right)\)
\(16x^2-24xy+9y^2\)
\(=\left(4x\right)^2-2.4x.3y+\left(3y\right)^2\)
\(=\left(4x-3y\right)^2\)
\(27x^3+125y^3=\left(3x\right)^3+\left(5y\right)^3=\left(3x+5y\right)\left(9x^2-15xy+25y^2\right)\)
\(16x^2-24xy+9y^2=\left(4x\right)^2-2\cdot4x\cdot3y+\left(3y\right)^2=\left(4x-4y\right)^2\)
\(16\left(4x+5\right)^2-25\left(2x+2\right)^2=\left[4\left(4x+5\right)\right]^2-\left[5\left(2x+2\right)\right]^2=\left(6x+10\right)\left(26x+30\right)\)
\(=4\left(3x+5\right)\left(13x+15\right)\)
