1: \(4x^2-9y^4=\left(2x-3y^2\right)\left(2x+3y^2\right)\)
2: \(8x^3+27y^3=\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)\)
3: \(25x^6-10x^3y^4+y^8=\left(5x^3-y^4\right)^2\)
4: \(-4x^2+20x-25=-\left(2x-5\right)^2\)
5: \(2x^3-72x=2x\left(x^2-36\right)=2x\left(x-6\right)\left(x+6\right)\)
6: \(16x^2-9\left(x+y\right)^2\)
\(=\left(4x\right)^2-\left(3x+3y\right)^2\)
\(=\left(4x-3x-3y\right)\left(4x+3y+3x\right)\)
\(=\left(x-3y\right)\left(7x+3y\right)\)
7: \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)
\(=\left(6x+9\right)^2-\left(2x+2\right)^2\)
\(=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)\)
\(=\left(4x+7\right)\left(8x+11\right)\)
8: Ta có: \(x^2-10x+25-4y^2\)
\(=\left(x-5\right)^2-\left(2y\right)^2\)
\(=\left(x-5-2y\right)\left(x-5+2y\right)\)
9: Ta có: \(16x^2-\left(x^2+4\right)^2\)
\(=\left(4x-x^2-4\right)\left(4x+x^2+4\right)\)
\(=-\left(x^2-4x+4\right)\left(x^2+4x+4\right)\)
\(=-\left(x-2\right)^2\cdot\left(x+2\right)^2\)
10: Ta có: \(\left(x^2+y^2\right)^2-4x^2y^2\)
\(=\left(x^2+2xy+y^2\right)\left(x^2-2xy+y^2\right)\)
\(=\left(x+y\right)^2\cdot\left(x-y\right)^2\)
11: Ta có: \(\left(x^2+y^2-8\right)^2-\left(2xy+8\right)^2\)
\(=\left(x^2+y^2-8-2xy-8\right)\left(x^2+y^2-8+2xy+8\right)\)
\(=\left[\left(x^2-2xy+y^2\right)-16\right]\left[\left(x+y\right)^2\right]\)
\(=\left(x+y\right)^2\cdot\left(x-y-4\right)\left(x-y+4\right)\)
12: Ta có: \(16\left(x+y\right)^2-9\left(x-5y\right)^2\)
\(=\left(4x+4y\right)^2-\left(3x-15y\right)^2\)
\(=\left(4x+4y-3x+15y\right)\left(4x+3y+3x-15y\right)\)
\(=\left(x+19y\right)\left(7x-12y\right)\)
13: Ta có: \(\left(x+y+z\right)^2-4z^2\)
\(=\left(x+y+z-2z\right)\left(x+y+z+2z\right)\)
\(=\left(x+y-z\right)\left(x+y+3z\right)\)
14: Ta có: \(x^3+6x^2y+9xy^2-4x\)
\(=x\left(x^2+6xy+9y^2-4\right)\)
\(=x\left[\left(x+3y\right)^2-4\right]\)
\(=x\left(x+3y-2\right)\left(x+3y+2\right)\)
