3H:
a: \(x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-\left(2xy\right)^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
=(x+y-2xy)(x+y+2xy)
b: \(49-a^2+2ab-b^2\)
\(=49-\left(a-b\right)^2\)
=(7-a+b)(7+a-b)
c: \(a^2-b^2+4bc-4c^2\)
\(=a^2-\left(b^2-4bc+4c^2\right)\)
\(=a^2-\left(b-2c\right)^2\)
=(a+b-2c)(a-b+2c)
d: \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc\right)^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\)
\(=\left\lbrack a^2-\left(b^2-2bc+c^2\right)\right\rbrack\left\lbrack\left(b^2+2bc+c^2\right)-a^2\right\rbrack\)
\(=\left\lbrack a^2-\left(b-c\right)^2\right\rbrack\left\lbrack\left(b+c\right)^2-a^2\right\rbrack\)
=(a-b+c)(a+b-c)(b+c-a)(b+c+a)
2H: \(N=x^2-2x-y^2+1\)
\(=x^2-2x+1-y^2\)
\(=\left(x-1\right)^2-y^2\)
=(x-1-y)(x-1+y)
1H:
\(M=x^2-3x+xy-3y\)
=x(x-3)+y(x-3)
=(x-3)(x+y)
