\(x^2+4xy+4y^2-4z^2-1-4z\)

\(=x^2+4xy+4y^2-\left(4z^2+4z+1\right)\)

\(=\left(x+2y\right)^2-\left(2z+1\right)^2\)

\(=\left(x+2y+2z+1\right)\left(x+2y-2z-1\right)\)

\(x^2+4y^2+9-4xy-6x+12y\)

\(=\left(x^2-4xy+4y^2\right)+\left(-6x+12y\right)+9\)

\(=\left(x-2y\right)^2-6\left(x-2y\right)+9\)

\(=\left(x-2y-3\right)^2\)

\(\left(x+2y-4\right)\left(x+2y+4\right)\)

(x+y)^2 - 5y^2

x^2- 4y^2 + 4xy

= x^2 + 4xy - 4y^2

=x^2 + 2x2y - (2y)^2

= ( x - 2y )^2

 x² - 4y² + 4xy = x² + 4xy - 4y² = - (x² - 4xy + 4y²) = - ((x² - 2x.2y + (2y)²)

= - ( x - 2y)²

\(x^2-25-4xy+4y^2\)

\(=\left(x^2-4xy+4y^2\right)-25\)

\(=\left[x^2-2\cdot x\cdot2y+\left(2y\right)^2\right]-25\)

\(=\left(x-2y\right)^2-5^2\)

\(=\left(x-2y-5\right)\cdot\left(x-2y+5\right)\)

\(-\left(x+2y\right)^2\)

\(-\left(x-3\right)^2\)

\(\left(3-5x\right)^2\)

\(-x^2-4xy-4y^2=-\left(x+2y\right)^2\)

\(-x^2+6x-9=-\left(x-3\right)^2\)

\(25x^2-30x+9=\left(5x-3\right)^2\)

1.A

2.C

3.B

4.C

a

c

b

c

(x-1)y^2-4(x-1)y