a) Ta có: \(x^2-2xy+y^2-4\)
\(=\left(x-y\right)^2-2^2\)
\(=\left(x-y-2\right)\left(x-y+2\right)\)
b) Ta có: \(-16x^2+8xy-y^2+49\)
\(=-\left(16x^2-8xy+y^2-49\right)\)
\(=-\left[\left(16x^2-8xy+y^2\right)-49\right]\)
\(=-\left[\left(4x-y\right)^2-7^2\right]\)
\(=-\left(4x-y-7\right)\left(4x-y+7\right)\)
c) Ta có: \(x^6-x^4+2x^3+2x^2\)
\(=x^4\left(x^2-1\right)+2x^2\left(x+1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)+2x^2\left(x+1\right)\)
\(=\left(x+1\right)\left[x^4\left(x-1\right)+2x^2\right]\)
\(=\left(x+1\right)\left(x^5-x^4+2x^2\right)\)
\(=\left(x+1\right)\left[\left(x^5+x^2\right)-\left(x^4-x^2\right)\right]\)
\(=\left(x+1\right)\left[x^2\left(x^3+1\right)-x^2\left(x^2-1\right)\right]\)
\(=x^2\cdot\left(x+1\right)\cdot\left(x^3+1-x^2+1\right)\)
\(=x^2\cdot\left(x+1\right)\cdot\left(x^3-x^2+2\right)\)
d) Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)
\(=\left[\left(x+y\right)-\left(x-y\right)\right]\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)
\(=\left(x+y-x+y\right)\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)
\(=2y\cdot\left(3x^2+y^2\right)\)
