8p2+24p+18

Factor 2 out of 8p2.

2(4p2)+24p+18

Factor 2 out of 24p.

2(4p2)+2(12p)+18

Factor 2 out of 18.

2(4p2)+2(12p)+2(9)

Factor 2 out of 2(4p2)+2(12p).

2(4p2+12p)+2(9)

Factor 2 out of 2(4p2+12p)+2(9).

2(4p2+12p+9)

2(4p2+12p+9)

Rewrite 4p2 as (2p)2.

2((2p)2+12p+9)

Rewrite 9 as 32.

2((2p)2+12p+32)

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

12p=2⋅(2p)⋅3

Rewrite the polynomial.

2((2p)2+2⋅(2p)⋅3+32)

Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=2p and b=3.

2(2p+3)2

2(2p+3)2

Factor 8p^2+24p+18