\(a,4x^2-12xy+9y^2\)
\(=\left(2x\right)^2-2.2x.3y+\left(3y\right)^2\)
\(=\left(2x-3y\right)^2\)
\(b,x^4+2x^2+1\)
\(=\left(x^2\right)^2+2.x^2.1+1^2\)
\(=\left(x^2+1\right)^2\)
\(c,a^4+4+4a\)
\(d,-x^2-2xy-y^2\)
\(=-\left(x^2+2xy+y^2\right)\)
\(=-\left(x+y\right)^2\)
\(e,10a-a^2-25\)
\(=-\left(a^2-10a+25\right)\)
\(=-\left(a^2-5a-5a+25\right)\)
\(=-\left[\left(a^2-5a\right)-\left(5a-25\right)\right]\)
\(=-\left[a\left(a-5\right)-5\left(a-5\right)\right]\)
\(=-a\left(a-5\right)+5\left(a-5\right)\)
\(=\left(a-5\right)\left(5-a\right)\)
\(g,a^2-2a+1\)
\(=a^2-2.a.1+1^2\)
\(=\left(a-1\right)^2\)
\(h,\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y-1\right)^2\)
