Bài 1:
a) Ta có: \(x^2y^2-1\)
\(=\left(xy\right)^2-1^2\)
\(=\left(xy-1\right)\left(xy+1\right)\)
b) Ta có: \(x^4y^4-z^4\)
\(=\left(x^2y^2\right)^2-\left(z^2\right)^2\)
\(=\left(x^2y^2-z^2\right)\left(x^2y^2+z^2\right)\)
\(=\left(xy-z\right)\left(x^2y^2+z^2\right)\left(xy+z\right)\)
c) Ta có: \(\left(x+a\right)^2-25\)
\(=\left(x+a\right)^2-5^2\)
\(=\left(x+a-5\right)\left(x+a+5\right)\)
d) Ta có: \(\left(x+a\right)^2-\left(y+b\right)^2\)
\(=\left(x+a-y-b\right)\left(x+a+y+b\right)\)
e) Ta có: \(x^2+2x+1-y^2+2y-1\)
\(=\left(x^2+2x+1\right)-\left(y^2-2y+1\right)\)
\(=\left(x+1\right)^2-\left(y-1\right)^2\)
\(=\left(x+1-y+1\right)\left(x+1+y-1\right)\)
\(=\left(x-y+2\right)\left(x+y\right)\)
g) Ta có: \(\left(x^2-2x+1\right)^3+y^6\)
\(=\left[\left(x-1\right)^2\right]^3+y^6\)
\(=\left(x-1\right)^6+y^6\)
\(=\left[\left(x-1\right)^2+y^2\right]\left[\left(x-1\right)^4-\left(x-1\right)^2\cdot y^2+y^4\right]\)
\(=\left(x^2-2x+1+y^2\right)\left(x^4-4x^3+6x^2-4x+1-x^2y^2+2xy^2-y^2+y^4\right)\)
k) Ta có: \(\left(x-a\right)^4+4a^4\)
\(=\left(x-a\right)^4+4a^4+2\cdot\left(x-a\right)^2\cdot2a^2-4\left[a\left(x-a\right)\right]^2\)
\(=\left(x-a+2a^2\right)^2-4\left(ax-a^2\right)^2\)
\(=\left(x-a+2a^2-2ax+2a^2\right)\left(x-a+2a^2+2ax-2a^2\right)\)
\(=\left(x-a-2ax+4a^2\right)\left(x-a+2ax\right)\)
