1: \(a^2+2a+1=\left(a+1\right)^2\)
2: \(4a^2-4ab+b^2=\left(2a-b\right)^2\)
3: \(4x^4-16x^2y^3+16y^6=4\left(x^2-4y^3\right)^2\)
4: \(-a^2+6a-9=-\left(a-3\right)^2\)
a) \(a^2+2a+1=\left(a+1\right)^2\)
b) \(4a^2-4ab+b^2=\left(2a-b\right)^2\)
c) \(4x^4-16x^2y^3+16y^6=\left(2x^2-4y^3\right)^2=4\left(x^2-2y^3\right)^2\)
d) \(-a^2+6a-9=-\left(a-3\right)^2\)
e) \(-9x^6+12x^7-4x^8=-x^6\left(9-12x+4x^2\right)=-x^6\left(3-2x\right)^2\)
f) \(\left(x+1\right)^2-2\left(x^2-1\right)+\left(x-1\right)^2=\left(x+1\right)^2-2\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2=\left(x+1-x+1\right)^2=2^2=4\)
