(x+2)(x-6)+16
=x^2-4x-12+16
=x^2-4x+4
=(x-2)^2
(x-y)^2+4xy
=x^2+y^2-2xy+4xy
=x^2+y^2+2xy
=(x+y)^2
2a(x^2+1)^2-2ax^2
=2a[(x^2+1)^2-x^2]
=2a(x^2+1-x)(x^2+1+x)
25(a+b)^2-9(a-b)^2
=[5(a+b)-3(a-b)][5(a+b)+3(a-b)]
=(5a+5b-3a+3b)(5a+5b+3a-3b)
=(2a+8b)(8a+2b)
=4(a+4b)(4a+b)
(a+3b)^2-10(a+3b)+25
=(a+3b-5)^2