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

Math
(5k+3)2-8(5k+3)+16
Let u=5k+3. Substitute u for all occurrences of 5k+3.
u2-8u+16
Factor using the perfect square rule.
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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

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