a: Ta có: \(x^2+2xy+y^2-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y+2xy\right)\left(x+y-2xy\right)\)
b: Ta có: \(49-a^2+2ab-b^2\)
\(=49-\left(a-b\right)^2\)
\(=\left(7-a+b\right)\left(7+a-b\right)\)
c: Ta có: \(a^2-b^2+4bc-4c^2\)
\(=a^2-\left(b-2c\right)^2\)
\(=\left(a-b+2c\right)\left(a+b-2c\right)\)
d: Ta có: \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\)
\(=-\left[\left(b^2-2bc+c^2\right)-a^2\right]\left[\left(b+c\right)^2-a^2\right]\)
\(=-\left(b-c-a\right)\left(b-c+a\right)\left(b+c-a\right)\left(b+c+a\right)\)
a) \(x^2-4x^2y^2+y^2+2xy=\left(x^2+2xy+y^2\right)-\left(2xy\right)^2=\left(x+y\right)^2-\left(2xy\right)^2=\left(x+2xy+y\right)\left(x-2xy+y\right)\)
b) \(49-a^2+2ab-b^2=49-\left(a^2-2ab+b^2\right)=7^2-\left(a-b\right)^2=\left(7+a-b\right)\left(7-a+b\right)\)
