Explanation:
Rewrite 9x2 as (3x)2
.
(3x)2+24x+16
Rewrite 16
as 42
.
(3x)2+24x+42
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
24x=2⋅(3x)⋅4
Rewrite the polynomial.
(3x)2+2⋅(3x)⋅4+42
Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2
, where a=3x and b=4
.
(3x+4)2