1.1
$x^2-2x+1=(x-1)^2$
1.2
$x^2+4x+4=x^2+2.2x+2^2=(x+2)^2$
1.3
$4x^2+4x+1=(2x)^2+2.2x+1=(2x+1)^2$
1.4
$4x^2-12x+9=(2x)^2-2.2x.3+3^2=(2x-3)^2$
1.5
$x^2-6x+9=x^2-2.3x+3^2=(x-3)^2$
1.6
$1+12x+36x^2=(6x)^2+2.6x+1=(6x+1)^2$
1.7
$9x^2-24xy+16y^2=(3x)^2-2.3x.4y+(4y)^2=(3x-4y)^2$
1.8.
$25x^2-20xy+4y^2=(5x)^2-2.5x.2y+(2y)^2=(5x-2y)^2$
1.9.
$25x^4-10x^2y+y^2=(5x^2)^2-2.5x^2.y+y^2=(5x^2-y)^2$
1.10
$\frac{x^2}{4}+2xy+4y^2=(\frac{x}{2})^2+2.\frac{x}{2}.2y+(2y)^2$
$=(\frac{x}{2}+2y)^2$
1.11
$6x-9-x^2=-(x^2-6x+9)=-(x-3)^2$
1.12
$10x-25-x^2=-(x^2-10x+25)=-(x-5)^2$
1.13
$12x-9x^2-4=-[9x^2-12x+4]=-[(3x)^2-2.3x.2+2^2]$
$=-(3x-2)^2$
1.14.
$-x^2-14x-49=-(x^2+14x+49)=-(x^2+2.7x+7^2)=-(x+7)^2$