(5k+3)2-8(5k+3)+16

Let u=5k+3. Substitute u for all occurrences of 5k+3.

u2-8u+16

Rewrite 16 as 42.

u2-8u+42

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

8u=2⋅u⋅4

Rewrite the polynomial.

u2-2⋅u⋅4+42

Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=u and b=4.

(u-4)2

(u-4)2

Replace all occurrences of u with 5k+3.

(5k+3-4)2

Subtract 4 from 3.

(5k-1)2

Factor (5k+3)^2-8(5k+3)+16